ICSE Class 7 Mathematics · Solutions for Class 7 RS Aggarwal ICSE Foundation Mathematics · 33 solved questions
12 bags of rice having equal weights weigh 174 kg. How much will 20 such bags weigh?
Weight of 12 bags = 174 kg.
Weight of 1 bag = $\Big(\frac{174}{12}\Big) \text{ kg}$
[Less bags, Less weight]
Weight of 20 bags = $\Big(\frac{174}{12} \times 20\Big) \text{ kg}$
[More bags, More weight]
= $\Big(\frac{174}{3} \times 5\Big)$ kg
= 58 x 5 kg $\quad$ (Dividing 174 and 3 by 3)
= 290 kg.
Hence, the weight of 20 bags is 290 kg.
8 kg of tomatoes cost ₹ 84. What is the cost of 14 kg of tomatoes?
Cost of 8 kg tomatoes = ₹ 84.
Cost of 1 kg tomato = ₹ $\Big(\frac{84}{8}\Big)$
[Less tomatoes, Less cost]
Cost of 14 kg tomatoes = ₹ $\Big(\frac{84}{8} \times 14\Big)$
[More tomatoes, More cost]
= ₹ $\Big(\frac{21}{2} \times 14\Big)$
= ₹ $\Big(\frac{294}{2}\Big)$
= ₹ 147
Hence, the cost of 14 kg of tomatoes is ₹ 147.
16 m of cloth costs ₹ 2200. What is the cost of 6 m of cloth?
Cost of 16 m of cloth = ₹ 2200.
Cost of 1 m of cloth = ₹ $\Big(\frac{2200}{16}\Big)$
[Less cloth, Less cost]
Cost of 6 m of cloth = ₹ $\Big(\frac{2200}{16} \times 6\Big)$
[More cloth, More cost]
$$\begin{aligned}= ₹ \Big(\frac{2200}{16} \times 6\Big) \\[1em] = ₹ \Big(\frac{275}{2} \times 6\Big) \quad \text{(Dividing 2200 and 16 by 8)} \\[1em] = ₹ \Big(\frac{1650}{2}\Big) \\[1em] = ₹ 825\end{aligned}$$
Hence, the cost of 6 m of cloth is ₹ 825.
If 8.5 m of a uniform rod weighs 30.6 kg, what will be the weight of 5 m of the same rod?
Weight of 8.5 m rod = 30.6 kg.
Weight of 1 m rod = $\Big(\frac{30.6}{8.5}\Big) \text{ kg}$
[Less length, Less weight]
Multiply by 10 to remove decimals.
Weight of 1 m rod = $\Big(\frac{30.6 \times 10}{8.5 \times 10}\Big) \text{ kg} = \Big(\frac{306}{85}\Big) \text{ kg}$
Weight of 5 m rod = $\Big(\frac{306}{85} \times 5\Big) \text{ kg}$
[More length, More weight]
= $\Big(\frac{306}{17}\Big) \text{ kg} \quad \text{(Dividing 5 and 85 by 5)}$
= 18 kg.
Hence, the weight of 5 m of the rod is 18 kg.
The cost of 6 purses is ₹ 453. How many such purses can be bought for ₹ 604?
For ₹ 453, number of purses bought = 6.
For ₹ 1, number of purses bought = $\Big(\frac{6}{453}\Big) \text{ purses}$
[Less money, Less purses]
For ₹ 604, number of purses bought = $\Big(\frac{6}{453} \times 604\Big) \text{ purses}$
[More money, More purses]
= $\Big(\frac{2}{151} \times 604\Big) \text{ purses} \quad \text{(Dividing 6 and 453 by 3)}$
= $\Big(\frac{1208}{151}\Big)$ purses
= 8 purses.
Hence, 8 purses can be bought for ₹ 604.
12 apples weigh 2 kg 500 g. How many apples will weigh 15 kg?
First, convert weight to a single unit:
1000 g = 1 kg
500 g = 0.5 kg
∴ 2 kg 500 g = (2 + 0.5) kg = 2.5 kg.
For 2.5 kg, number of apples = 12.
For 1 kg, number of apples = $\Big(\frac{12}{2.5}\Big)$
[Less weight, Less apples]
Multiply by 10 to remove decimals.
For 1 kg, number of apples = $\Big(\frac{12 \times 10}{2.5 \times 10}\Big) = \Big(\frac{120}{25}\Big)$ apples
For 15 kg, number of apples = $\Big(\frac{120}{25} \times 15\Big) \text{ apples}$
[More weight, More apples]
= $\Big(\frac{120}{5} \times 3\Big) \text{ apples} \quad \text{(Dividing 15 and 25 by 5)}$
= 24 x 3 apples $\quad$ (Dividing 120 and 5 by 5)
= 72 apples.
Hence, 72 apples will weigh 15 kg.
55 m of cloth is required to make 25 shirts. How much cloth will be required to make 35 shirts of the same size?
Cloth required for 25 shirts = 55 m.
Cloth required for 1 shirt = $\Big( \frac{55}{25}\Big) \text{m}$
[Less shirts, Less cloth]
Cloth required for 35 shirts = $\Big( \frac{55}{25} \times 35\Big) \text{m}$
[More shirts, More cloth]
= $\Big( \frac{55}{5} \times 7\Big)$ m
= 11 x 7 m $\quad$ (Dividing 55 and 5 by 5)
= 77 m.
Hence, 77 m of cloth will be required to make 35 shirts.
A scooter consumes 2.5 litres of petrol in covering a distance of 85 km. What distance will it cover in 8 litres of petrol?
In 2.5 litres, distance covered = 85 km.
In 1 litre, distance covered = $\Big( \frac{85}{2.5}\Big)$ km.
[Less petrol, Less distance]
Multiply by 10 to remove decimals.
In 1 litre, distance covered = $\Big( \frac{85 \times 10}{2.5 \times 10}\Big) = \Big( \frac{850}{25}\Big)$ km
In 8 litres, distance covered = $\Big( \frac{850}{25} \times 8\Big) \text{ km}$
[More petrol, More distance]
= 34 x 8 km $\quad$ (Dividing 850 and 25 by 25)
= 272 km.
Hence, the scooter will cover 272 km in 8 litres of petrol.
A journey of 124 km costs ₹ 1395. How much will a journey of 240 km cost?
Cost of 124 km journey = ₹ 1395.
Cost of 1 km journey = ₹ $\Big(\frac{1395}{124}\Big)$
[Less distance, Less cost]
Cost of 240 km journey = ₹ $\Big(\frac{1395}{124} \times 240\Big)$
[More distance, More cost]
= ₹ 11.25 x 240 $\quad$ (Dividing 1395 and 124 by 124)
= ₹ 2700
Hence, a journey of 240 km will cost ₹ 2700.
A compositor takes 1 hour 45 minutes to compose 24 pages of a book. How long will he take to compose 64 pages?
First, convert time into minutes:
1 hour = 60 minutes
∴ 1 hour 45 minutes = 60 + 45 = 105 minutes.
Time taken to compose 24 pages = 105 minutes.
Time taken to compose 1 page = $\Big( \frac{105}{24}\Big) \text{ minutes}$
[Less pages, Less time]
Time taken to compose 64 pages = $\Big(\frac{105}{24} \times 64\Big) \text{ minutes}$
[More pages, More time]
= $\Big(\frac{105}{3} \times 8\Big) \text{ minutes} \quad \text{(Dividing 24 and 64 by 8)}$
= 35 x 8 minutes
= 280 minutes (or 4 hours 40 minutes)
Hence, he will take 4 hours 40 minutes to compose 64 pages.
If a man walks 16 km in 5 hours, how long would he take to walk 11.2 km?
Time taken to walk 16 km = 5 hours.
Time taken to walk 1 km = $\Big(\frac{5}{16}\Big) \text{ hours}$
[Less distance, Less time]
Time taken to walk 11.2 km = $\Big(\frac{5}{16} \times 11.2\Big) \text{ hours}$
[More distance, More time]
= $\Big(\frac{5 \times 11.2}{16}\Big)$ hours
= $\frac{56}{16}$ hours
= 3.5 hours (or 3 hours 30 minutes).
Time taken to walk 11.2 km = 3 hours 30 minutes
5 men can paint a hall in 18 hours. How many men will be able to paint it in 10 hours?
Men required to paint in 18 hours = 5 men.
Men required to paint in 1 hour = (5 x 18) men.
[Less time, More men]
Men required to paint in 10 hours = $\Big(\frac{5 \times 18}{10}\Big) \text{ men}$
[More time, Less men]
= $\frac{90}{10}$ men
= 9 men.
9 men are required to paint in 10 hours.
30 workers can dig a trench in 5 days. How many workers will be required to dig it in 6 days?
Workers required to dig in 5 days = 30 workers.
Workers required to dig in 1 day = (30 x 5) workers.
[Less days, More workers]
Workers required to dig in 6 days = $\Big(\frac{30 \times 5}{6}\Big) \text{ workers}$
[More days, Less workers]
= (5 x 5) workers $\quad$ [Dividing 30 and 6 by 6]
= 25 workers.
25 workers are required to dig in 6 days.
In a fort, 360 men had provisions for 21 days. If 60 more men join them, how long will the provisions last?
Original men = 360.
New men = 360 + 60 = 420.
Provisions for 360 men last = 21 days.
Provisions for 1 man last = (21 x 360) days.
[Less men, More days]
Provisions for 420 men last = $\Big(\frac{21 \times 360}{420}\Big) \text{ days}$
[More men, Less days]
= $\Big(\frac{1 \times 360}{20}\Big) \text{ days} \quad \text{[Dividing 21 and 420 by 21]}$
= 18 days.
420 men had provisions for 18 days.
In an army camp, 300 soldiers had provisions for 13 days. If 40 of them are transferred to the other camp, how long will the provisions last?
Original soldiers = 300.
Remaining soldiers = 300 - 40 = 260.
Provisions for 300 soldiers last = 13 days.
Provisions for 1 soldier last = (13 x 300) days.
[Less soldiers, More days]
Provisions for 260 soldiers last = $\Big(\frac{13 \times 300}{260}\Big) \text{ days}$
[More soldiers, Less days]
= $\Big(\frac{1 \times 300}{20}\Big) \text{ days} \quad \text{[Dividing 13 and 260 by 13]}$
= 15 days.
260 soldiers had provisions for 15 days
Moving at the rate of 70 km/hr, a car completes a journey in 18 minutes. How long would it take to complete this journey, if the speed is increased to 84 km/hr?
Time taken at 70 km/hr speed = 18 minutes.
Time taken at 1 km/hr speed = (18 x 70) minutes.
[Less speed, More time]
Time taken at 84 km/hr speed = $\Big(\frac{18 \times 70}{84}\Big) \text{ minutes}$
[More speed, Less time]
= $\Big(\frac{3 \times 70}{14}\Big) \text{ minutes} \quad$ [Dividing 18 and 84 by 6]
= 3 x 5 minutes $\quad$ [Dividing 70 and 14 by 14]
= 15 minutes.
At the rate of 84 km/hr, the car completes the journey in 15 minutes.
If 15 men can level a ground in 60 days, in how many days can 36 men level the same ground?
Given:
Days taken by 15 men = 60 days
Days taken by 1 man = 60 x 15 days
[Less men, More days]
Days taken by 36 men = $\Big(\frac{60 \times 15}{36}\Big) \text{ days}$
[More men, Less days]
= $\Big(\frac{5 \times 15}{3}\Big) \text{ days} \quad \text{[Dividing 60 and 36 by 12]}$
= 5 x 5 days $\quad$ [Dividing 15 and 3 by 3]
= 25 days
Hence, option 2 is the correct option.
If 150 m of cloth is required to prepare dresses for 42 women, then for how many women will 125 m of cloth be sufficient?
Given:
Number of women for 150 m cloth = 42 women
Number of women for 1 m cloth = $\frac{42}{150} \text{ women}$
[Less cloth, Less women]
Number of women for 125 m cloth = $\Big(\frac{42}{150} \times 125\Big) \text{ women}$
[More cloth, More women]
= $\Big(\frac{42}{6} \times 5\Big) \text{ women} \quad \text{[Dividing 125 and 150 by 25]}$
= 7 x 5 women $\quad$ [Dividing 42 and 6 by 6]
= 35 women
Hence, option 3 is the correct option.
In a map, 1.5 cm represents 46.8 km. How much distance will be represented by 3.5 cm on the map?
Given:
Distance for 1.5 cm = 46.8 km
Distance for 1 cm = $\frac{46.8}{1.5} \text{ km}$
[Less cm, Less distance]
Distance for 3.5 cm = $\Big(\frac{46.8}{1.5} \times 3.5\Big) \text{ km}$
[More cm, More distance]
Multiply by 10 to remove decimals:
= $\Big(\frac{46.8 \times 10}{1.5 \times 10} \times 3.5\Big) \text{ km} = \Big(\frac{468}{15} \times 3.5\Big)$ km
= 31.2 x 3.5 km $\quad$ [Dividing 468 and 15 by 15]
= 109.2 km
Hence, option 3 is the correct option.
If a car can go 224 km in 20 litres of petrol, how far can it go in 32.5 litres of petrol?
Distance on 20 L = 224 km
Distance on 1 L = $\frac{224}{20} \text{ km}$
[Less petrol, Less distance]
Distance on 32.5 L = $\Big(\frac{224}{20} \times 32.5\Big) \text{ km}$
[More petrol, More distance]
= 11.2 x 32.5 km $\quad$ [Dividing 224 and 20 by 20]
= 364 km
Hence, option 1 is the correct option.
If 16 buffaloes eat as much as 28 cows, how many buffaloes eat as much as 91 cows?
Buffaloes for 28 cows = 16 Buffaloes
Buffaloes for 1 cow = $\frac{16}{28} \text{ Buffaloes}$
[Less cows, Less buffaloes]
Buffaloes for 91 cows = $\Big(\frac{16}{28} \times 91\Big) \text{ Buffaloes}$
[More cows, More buffaloes]
= $\frac{4}{7} \times 91 \text{ Buffaloes} \quad \text{[Dividing 16 and 28 by 4]}$
= 4 x 13 Buffaloes $\quad$ [Dividing 91 and 7 by 7]
= 52 Buffaloes
Hence, option 2 is the correct option.
Fill in the blanks :
(i) If 6 pens cost ₹ 69, then the cost of 16 pens is ............... .
(ii) If 1 dozen eggs cost ₹ 54, then a tray of 30 eggs will cost ............... .
(iii) A worker is paid ₹ 1610 as wages for 14 days. His wages for 30 days will be ............... .
(iv) 25 boxes of 12 ice-cream cups each, cost ₹ 10500. The cost of 15 boxes of 20 ice-cream cups each, will be ............... .
(i) If 6 pens cost ₹ 69, then the cost of 16 pens is ₹ 184.
(ii) If 1 dozen eggs cost ₹ 54, then a tray of 30 eggs will cost ₹ 135.
(iii) A worker is paid ₹ 1610 as wages for 14 days. His wages for 30 days will be ₹ 3450.
(iv) 25 boxes of 12 ice-cream cups each, cost ₹ 10500. The cost of 15 boxes of 20 ice-cream cups each, will be ₹ 10500.
Explaination
(i) Given:
Cost of 6 pens = ₹ 69
Cost of 1 pen = ₹ $\Big( \frac{69}{6} \Big)$
[Less pens, Less cost]
Cost of 16 pens = ₹ $\Big( \frac{69}{6} \times 16 \Big)$
[More pens, More cost]
= ₹ $\Big( \frac{23}{2} \times 16 \Big)$
= ₹ 23 x 8 $\quad$ [Dividing 16 and 2 by 2]
= ₹ 184
(ii) Given:
1 dozen = 12 eggs
Cost of 12 eggs = ₹ 54
Cost of 1 egg = ₹ $\Big( \frac{54}{12} \Big) \quad \text{[Less eggs, Less cost]}$
Cost of 30 eggs = ₹ $\Big( \frac{54}{12} \times 30 \Big)$
[More eggs, Less More]
= ₹ $\Big( \frac{54}{2} \times 5 \Big) \quad \text{[Dividing 30 and 12 by 6]}$
= ₹ 27 x 5 $\quad$ [Dividing 54 and 2 by 2]
= ₹ 135
(iii) Given:
Wages for 14 days = ₹ 1610
Wages for 1 day = ₹ $\Big( \frac{1610}{14} \Big)$
[Less days, Less wages]
Wages for 30 days = ₹ $\Big( \frac{1610}{14} \times 30 \Big)$
[More days, More wages]
= ₹ 115 x 30 $\quad$ [Dividing 1610 and 14 by 14]
= ₹ 3450
(iv) Given:
Let us find the total number of cups first
25 boxes x 12 cups = 300 cups
Cost of 300 cups = ₹ 10500
Cost of 1 cup = ₹ $\frac{10500}{300} = ₹ 35$
[Less cups, Less cost]
15 boxes x 20 cups = 300 cups
Cost of 300 cups = ₹ 35 x 300
[More cups, More cost]
= ₹ 10500
Writer true (T) or false (F) :
(i) 12 kg apples for ₹ 2160 is a better buy than 15 kg apples for ₹ 2850.
(ii) If 7 men can finish a work in 84 days, then 12 men can finish the same work in 96 days.
(iii) If 9 notebooks cost ₹ 315, then the cost of 20 notebooks is ₹ 700.
(iv) In an indirect proportion, a decrease in one quantity causes an increase in the other quantity.
(i) True
Reason — Compare cost per kg
12 kg for ₹2160:
Cost of 1 kg = 2160 ÷ 12 = ₹ 180 per kg
Now, 15 kg for ₹2850:
Cost of 1 kg = 2850 ÷ 15 = ₹ 190 per kg
Since ₹ 180 is cheaper than ₹ 190, the first option is indeed a better buy.
(ii) False
Reason — Days for 7 men = 84 days
Days for 1 man = (84 x 7) days = 588 days $\quad \text{[Less men, More days]}$
Days for 12 men = 588 ÷ 12 = 49 days $\quad \text{[More men, Less days]}$
The statement says 96 days, which is mathematically impossible because increasing the number of men must decrease the time taken.
(iii) True
Reason — Cost of 9 notebook = ₹ 315
Cost of 1 notebook = ₹ $\frac{315}{9} = ₹ 35$
[Less notebooks, Less cost]
Cost of 20 notebooks = ₹ 35 x 20 = ₹ 700
[More notebooks, More cost]
The calculation matches the statement perfectly.
(iv) True
Reason — This is the fundamental definition of Indirect (Inverse) Proportion. As one value goes down, the related value must go up to maintain the constant product (x x y = k).
Rajan runs a typing company that processes the manuscript obtained from publishing companies. There are two processes in his work - typing and typesetting. He owns a team each for the two processes. He received a manuscript from a publishing company RBC. He knows that his team of 25 typists can type 225 pages in a day. Also, his team of 7 typesetters can typeset 90 pages in 5 days.
(1) If the manuscript from RBC needs 1350 pages to be typed, how many days will Rajan's team take to type it ?
(2) If Rajan employs 5 more typists in his team, in how many days can the work of RBC be completed ?
(3) In how many days will Rajan’s team of typesetters typeset the work from RBC ?
(4) If typesetting work begins only after the typing work is finished, what is the least number of days Rajan needs to get the work from RBC done by his existing team of 30 typists and 7 typesetters ?
(1) Given:
Number of typists = 25
Pages typed in 1 day = 225
Total manuscript pages to be typed = 1350
Days taken to type 1350 pages = $\frac{\text{Total pages}}{\text{Pages typed in 1 day}}$
Substituting the values in above, we get:
Days taken to type 1350 pages = $\frac{1350}{225}$
Days taken to type 1350 pages = 6 days
Hence, option 2 is the correct option.
(2) Given:
Original typists = 25
New typists added = 5
Total typists = 25 + 5 = 30
Typing rate of 25 typists = 225 pages per day
Rate of 1 typist = $\frac{225}{25} = 9$ pages per day
Rate of 30 typists = 30 x 9 = 270 pages per day
Days taken for 1350 pages = $\frac{\text{Total pages}}{\text{Pages typed in 1 day}}$
Substituting the values in above, we get:
Days taken for 1350 pages = $\frac{1350}{270}$
Days taken for 1350 pages = 5 days
Hence, option 2 is the correct option.
(3) Given:
Number of typesetters = 7
Pages typeset = 90
Time taken = 5 days
Total manuscript pages = 1350
Pages typeset by 7 typesetters in 1 day = $\frac{90}{5}$ = 18 pages
Days taken for 1350 pages = $\frac{\text{Total pages}}{\text{Pages typeset in 1 day}}$
Substituting the values in above, we get:
Days taken for 1350 pages = $\frac{1350}{18}$
Days taken for 1350 pages = 75 days
Hence, option 3 is the correct option.
(4) Given:
Time taken by 30 typists = 5 days $\quad$[From step 2]
Time taken by 7 typesetters = 75 days $\quad$[From step 3]
Condition: Typesetting starts after typing finishes.
Total days = Typing days + Typesetting days
= 5 + 75
= 80 days
Hence, option 2 is the correct option.
Assertion: When x and y are in indirect proportion, then (x + 1) and (y + 1) are also in indirect proportion.
Reason: Two quantities x and y are said to be in indirect proportion, if xy = k, where k is a constant.
Assertion (A) is false but Reason (R) is true.
Explanation
Let's test Assertion with numbers. If x = 2 and y = 6 (where xy = 12) and then x = 3 and y = 4 (where xy = 12), they are in indirect proportion.
Now add 1: (2+1) = 3 and (6+1) = 7. Here, 3 x 7 = 21.
Next set: (3+1) = 4 and (4+1) = 5. Here, 4 x 5 = 20.
Since $21 \neq 20$, the product is not constant. Therefore, (x+1) and (y+1) are not in indirect proportion. Assertion is False.
Hence, option 4 is the correct option.
Assertion: When the speed is kept fixed, time and distance are in direct proportion.
Reason: Two quantities are said to be in direct proportion if the increase (decrease) in one quantity causes the increase (decrease) in the other quantity.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Explanation
The formula for distance is Distance = Speed x Time. If speed is constant, doubling the time will exactly double the distance. Thus, they are in direct proportion ($\frac{D}{T} = \text{Speed}$). Assertion is True.
Reason is the fundamental definition of direct proportion. Reason is True.
The reason explains why the assertion is true: because as you spend more time traveling at a fixed speed, your distance increases accordingly.
Hence, option 1 is the correct option.
If 16 buffaloes eat as much as 28 cows, how many buffaloes eat as much as 91 cows?
Given:
16 buffaloes eat as much as 28 cows.
This is a case of direct proportion - more cows will be equivalent to more buffaloes.
Step 1: Find the number of buffaloes that eat as much as 1 cow
28 cows eat as much as 16 buffaloes.
1 cow eats as much as $\frac{16}{28}$ buffaloes. $\quad$[Less cows, Less buffaloes]
Step 2: Find the number of buffaloes that eat as much as 91 cows
91 cows eat as much as $\left(\frac{16}{28} \times 91\right)$ buffaloes. $\quad$[More cows, More buffaloes]
= $\frac{16 \times 91}{28}$
= $\frac{1456}{28}$
= 52
∴ 52 buffaloes eat as much as 91 cows.
Hence, option 2 is the correct option.
Monika received a salary of ₹18,200 for February 2014. How many days will she have to work to get another ₹14,950?
Given:
Salary received by Monika for February 2014 = ₹18,200
Number of days in February 2014 = 28
[∵ 2014 is not a leap year]
This is a case of direct proportion - more days of work, more salary earned.
Step 1: Find the salary for 1 day
Salary for 28 days = ₹18,200
Salary for 1 day = ₹$\frac{18200}{28}$
[Less days, Less salary]
= ₹650
Step 2: Find the number of days to earn ₹14,950
Salary for 1 day = ₹650
Number of days to earn ₹14,950 = $\frac{14950}{650}$
[More salary, More days]
= 23 days
∴ Monika will have to work for 23 days to earn ₹14,950.
Hence, option 3 is the correct option.
Amit took a loan of ₹500 from a local moneylender, and Kabeer took the same amount from a cooperative society. Amit paid ₹11 every day for 55 days to repay the loan. Kabeer paid ₹600 to the bank after 55 days. Both the loans were closed by 55 days. Who has paid more amount and by how much?
Given:
Loan amount taken by Amit = ₹500
Daily repayment by Amit = ₹11
Number of days for which Amit paid = 55
Amount paid by Kabeer after 55 days = ₹600
Step 1: Find the total amount paid by Amit
Amit paid ₹11 every day for 55 days.
Total amount paid by Amit = 11 × 55
= ₹605
Step 2: Compare the amounts paid by Amit and Kabeer
Amount paid by Amit = ₹605
Amount paid by Kabeer = ₹600
Difference = 605 − 600 = ₹5
Since ₹605 > ₹600, Amit paid ₹5 more than Kabeer.
∴ Amit paid ₹5 more than Kabeer.
Hence, option 2 is the correct option.
In a 50-over game of cricket, Team A scored only 3.6 runs per over in the first 15 overs. What should be the runs per over in the remaining 35 overs to reach the target of 299 runs?
Given:
Total overs in the game = 50
Runs per over in the first 15 overs = 3.6
Target = 299 runs
Step 1: Find the runs scored in the first 15 overs
Runs scored in 15 overs = 3.6 × 15
= 54 runs
Step 2: Find the runs needed in the remaining overs
Remaining runs = Target − Runs scored in first 15 overs
= 299 − 54
= 245 runs
Remaining overs = 50 − 15 = 35 overs
Step 3: Find the required runs per over
Required runs per over = $\frac{\text{Remaining runs}}{\text{Remaining overs}}$
= $\frac{245}{35}$
= 7 runs per over
∴ Team A should score 7 runs per over in the remaining 35 overs to reach the target.
Hence, option 3 is the correct option.
The cost of 2 dozen bananas is ₹240, and the cost of 18 lemons is ₹90. The ratio of the cost of 1 lemon to that of 1 banana is:
Given:
Cost of 2 dozen bananas = ₹240
Cost of 18 lemons = ₹90
1 dozen = 12, so 2 dozen = 24 bananas.
Step 1: Find the cost of 1 banana
Cost of 24 bananas = ₹240
Cost of 1 banana = ₹$\frac{240}{24}$
[Less bananas, Less cost]
= ₹10
Step 2: Find the cost of 1 lemon
Cost of 18 lemons = ₹90
Cost of 1 lemon = ₹$\frac{90}{18}$
[Less lemons, Less cost]
= ₹5
Step 3: Find the ratio of the cost of 1 lemon to that of 1 banana
Ratio = Cost of 1 lemon : Cost of 1 banana
= 5 : 10
$$\begin{aligned}= \frac{5}{10} \quad \text{[Writing the ratio as a fraction]} \\[1em] = \frac{1}{2} \\[1em] = 1 : 2\end{aligned}$$
∴ The ratio of the cost of 1 lemon to that of 1 banana is 1 : 2.
Hence, option 1 is the correct option.
At a particular time of a day, a 7 m high flagstaff casts a shadow which is 8.2 m long. What is the height of the building which casts a shadow of 20.5 m in length at the same moment?
Given:
Height of flagstaff = 7 m
Length of shadow of flagstaff = 8.2 m
Length of shadow of building = 20.5 m
This is a case of direct proportion - more shadow length, more height.
Step 1: Find the height corresponding to 1 m shadow
For 8.2 m shadow, height = 7 m
For 1 m shadow, height = $\frac{7}{8.2}$ m
[Less shadow, Less height]
Step 2: Find the height of the building corresponding to 20.5 m shadow
For 20.5 m shadow, height = $\left(\frac{7}{8.2} \times 20.5\right)$ m
[More shadow, More height]
= $\frac{7 \times 20.5}{8.2}$
= $\frac{143.5}{8.2}$
= 17.5 m
∴ The height of the building is 17.5 m.
Hence, option 2 is the correct option.
Ruchi types 40 words per minute and takes 24 minutes to type a certain document. Her friend Geeta has a typing speed of 48 words per minute. In how much time will she be able to type the same document?
Given:
Ruchi's typing speed = 40 words per minute
Time taken by Ruchi = 24 minutes
Geeta's typing speed = 48 words per minute
This is a case of indirect proportion - more typing speed, less time taken to type the same document.
Step 1: Find the total number of words in the document
Total words = Typing speed × Time taken
= 40 × 24
= 960 words
Step 2: Find the time taken by Geeta to type the document
Geeta types 48 words in 1 minute.
Geeta types 1 word in $\frac{1}{48}$ minute. $\quad$[Less words, Less time]
Geeta types 960 words in $\left(\frac{1}{48} \times 960\right)$ minutes. $\quad$[More words, More time]
= $\frac{960}{48}$
= 20 minutes
∴ Geeta will take 20 minutes to type the same document.
Hence, option 3 is the correct option.
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