ICSE Class 6 Mathematics · Solutions for Class 6 RS Aggarwal ICSE Foundation Mathematics · 28 solved questions
The cost of 11 pens is ₹253. Find:
(i) the cost of 1 pen.
(ii) the cost of 24 pens.
By the unitary method, we have:
Cost of 11 pens = ₹ 253
(i) Cost of 1 pen = ₹ $\Big(\frac{253}{11}\Big)$ = ₹ 23 [Less pens, Less cost]
Hence, cost of 1 pen = ₹ 23.
(ii) Cost of 24 pens = ₹ (23 x 24) = ₹ 552 [More pens, More cost]
Hence, cost of 24 pens = ₹ 552.
14 tins contain 210 litres of oil. How much oil is contained in (i) 1 tin, (ii) 18 tins?
By the unitary method, we have:
Oil contained in 14 tins = 210 litres
(i) Oil contained in 1 tin = $\Big(\frac{210}{14}\Big)$ litres = 15 litres [Less tins, Less oil]
Hence, 1 tin contains 15 litres of oil.
(ii) Oil contained in 18 tins = (15 x 18) litres = 270 litres [More tins, More oil]
Hence, 18 tins contain 270 litres of oil.
On 16 litres of diesel, a car runs 192 km. How many kilometres will it run on (i) 1 litre, (ii) 25 litres?
By the unitary method, we have:
On 16 litres of diesel, the car runs = 192 km
(i) On 1 litre of diesel, the car runs = $\Big(\frac{192}{16}\Big)$ km = 12 km [Less diesel, Less distance]
Hence, the car will run 12 km on 1 litre of diesel.
(ii) On 25 litres of diesel, the car runs = (12 x 25) km = 300 km [More diesel, More distance]
Hence, the car will run 300 km on 25 litres of diesel.
If 8 kg rice costs ₹620, what will be the cost of 18 kg of rice?
Cost of 8 kg of rice = ₹ 620
Cost of 1 kg of rice = ₹ $\Big(\frac{620}{8}\Big)$ [Less rice, Less cost]
Cost of 18 kg of rice = ₹ $\Big(\frac{620}{8} \times 18 \Big)$ = ₹ 1395 [More rice, More cost]
Hence, the cost of 18 kg of rice is ₹ 1395.
If the cost of 13 m of cloth is ₹1664, what will be the cost of 15 m of the same cloth?
Cost of 13 m of cloth = ₹ 1664
Cost of 1 m of cloth = ₹ $\Big(\frac{1664}{13}\Big)$ = ₹ 128 [Less cloth, Less cost]
Cost of 15 m of cloth = ₹ (128 x 15) = ₹ 1920 [More cloth, More cost]
Hence, the cost of 15 m of cloth is ₹ 1920.
If 15 tins of the same size contain 235 l of oil, how much oil will be there in 12 such tins?
Oil contained in 15 tins = 235 l
Oil contained in 1 tin = $\Big(\frac{235}{15}\Big) \text{ l }= \Big(\frac{47}{3}\Big)$ l [Less tins, Less oil]
Oil contained in 12 tins = $\Big(\frac{47}{3} \times 12 \Big)$ l = (47 x 4) l = 188 l [More tins, More oil]
Hence, 12 such tins will contain 188 litres of oil.
If 6 m of a uniform iron rod weighs 21 kg, what will be the weight of 20 m of the same rod?
Weight of 6 m of the rod = 21 kg
Weight of 1 m of the rod = $\Big(\frac{21}{6}\Big) \text{ kg }= \Big(\frac{7}{2}\Big)$ kg [Less length, Less weight]
Weight of 20 m of the rod = $\Big(\frac{7}{2} \times 20 \Big)$ kg = 70 kg [More length, More weight]
Hence, the weight of 20 m of the rod is 70 kg.
The weight of 63 books of the same size is 28 kg. How many such books will weigh 60 kg?
Number of books weighing 28 kg = 63
Number of books weighing 1 kg = $\Big(\frac{63}{28}\Big) = \Big(\frac{9}{4}\Big)$ [Less weight, Less books]
Number of books weighing 60 kg = $\Big(\frac{9}{4} \times 60 \Big)$ = (9 x 15) = 135 [More weight, More books]
Hence, 135 such books will weigh 60 kg.
If the cost of 25 bananas is ₹95, how many bananas can be bought for ₹152?
For ₹ 95, bananas bought = 25
For ₹ 1, bananas bought = $\Big(\frac{25}{95}\Big) = \Big(\frac{5}{19}\Big)$ [Less money, Less bananas]
For ₹ 152, bananas bought = $\Big(\frac{5}{19} \times 152 \Big)$ = (5 x 8) = 40 [More money, More bananas]
Hence, 40 bananas can be bought for ₹ 152.
15 boxes of the same size contain 1080 pens. How many such boxes will be needed for 1800 pens?
Number of boxes needed for 1080 pens = 15
Number of boxes needed for 1 pen = $\Big(\frac{15}{1080}\Big) = \Big(\frac{1}{72}\Big)$ [Less pens, Less boxes]
Number of boxes needed for 1800 pens = $\Big(\frac{1}{72} \times 1800 \Big)$ = 25 [More pens, More boxes]
Hence, 25 such boxes will be needed for 1800 pens.
A car travels 204 km in 9 hours. How long will it take to travel 340 km?
Time taken to travel 204 km = 9 hours
Time taken to travel 1 km = $\Big(\frac{9}{204}\Big) \text{ hours }= \Big(\frac{3}{68}\Big)$ hours [Less distance, Less time]
Time taken to travel 340 km = $\Big(\frac{3}{68} \times 340 \Big)$ hours = (3 x 5) hours = 15 hours [More distance, More time]
Hence, the car will take 15 hours to travel 340 km.
A bus consumes 12.5 litres of diesel in covering a distance of 65 km. How much diesel will it consume in covering 416 km?
In covering 65 km, diesel consumed = 12.5 litres
In covering 1 km, diesel consumed = $\Big(\frac{12.5}{65}\Big)$ litres [Less distance, Less diesel]
In covering 416 km, diesel consumed = $\Big(\frac{12.5}{65} \times 416 \Big) \text{ litres }= \Big(\frac{5200}{65}\Big)$ litres = 80 litres [More distance, More diesel]
Hence, the bus will consume 80 litres of diesel in covering 416 km.
44 metres of cloth is required to make 20 shirts. How much cloth will be required to make 35 such shirts?
For 20 shirts, cloth required = 44 m
For 1 shirt, cloth required = $\Big(\frac{44}{20}\Big) \text{ m }= \Big(\frac{11}{5}\Big)$ m [Less shirts, Less cloth]
For 35 shirts, cloth required = $\Big(\frac{11}{5} \times 35 \Big)$ m = (11 x 7) m = 77 m [More shirts, More cloth]
Hence, 77 m of cloth will be required to make 35 shirts.
18 bags of rice having equal weights weigh 297 kg. How much will 22 such bags weigh?
Weight of 18 bags = 297 kg
Weight of 1 bag = $\Big(\frac{297}{18}\Big) \text{ kg }= \Big(\frac{33}{2}\Big)$ kg [Less bags, Less weight]
Weight of 22 bags = $\Big(\frac{33}{2} \times 22 \Big)$ kg = (33 x 11) kg = 363 kg [More bags, More weight]
Hence, 22 such bags will weigh 363 kg.
If a man walks 14 km in 5 hours, how long would he take to walk 22.4 km?
Time taken to walk 14 km = 5 hours
Time taken to walk 1 km = $\Big(\frac{5}{14}\Big)$ hours [Less distance, Less time]
Time taken to walk 22.4 km = $\Big(\frac{5}{14} \times 22.4 \Big) \text{ hours }= \Big(\frac{112}{14}\Big)$ hours = 8 hours [More distance, More time]
Hence, the man would take 8 hours to walk 22.4 km.
If the cost of 14 pens is ₹378, what is the cost of 8 such pens?
Cost of 14 pens = ₹ 378
Cost of 1 pen = ₹ $\Big(\frac{378}{14}\Big)$ = ₹ 27 [Less pens, Less cost]
Cost of 8 pens = ₹ (27 x 8) = ₹ 216 [More pens, More cost]
Hence, option 3 is the correct option.
A rail journey of 50 km costs ₹160. How much will a journey of 80 km cost?
Cost of a journey of 50 km = ₹ 160
Cost of a journey of 1 km = ₹ $\Big(\frac{160}{50}\Big) = \Big(\frac{16}{5}\Big)$ [Less distance, Less cost]
Cost of a journey of 80 km = ₹ $\Big(\frac{16}{5} \times 80 \Big)$ = ₹ (16 x 16) = ₹ 256 [More distance, More cost]
Hence, option 2 is the correct option.
A car consumes 6 litres of petrol in covering 81 km. How much distance will it cover in 10 litres?
In 6 litres of petrol, distance covered = 81 km
In 1 litre of petrol, distance covered = $\Big(\frac{81}{6}\Big) \text{ km }= \Big(\frac{27}{2}\Big)$ km [Less petrol, Less distance]
In 10 litres of petrol, distance covered = $\Big(\frac{27}{2} \times 10 \Big)$ km = (27 x 5) km = 135 km [More petrol, More distance]
Hence, option 3 is the correct option.
A car covers 450 km in $4\frac{1}{2}$ hours. How much time will it take in covering 350 km?
Time taken to cover 450 km = $4\frac{1}{2} \text{ hours }= \Big(\frac{9}{2}\Big)$ hours
Time taken to cover 1 km = $\Big(\frac{9}{2} \times \frac{1}{450}\Big) \text{ hours }= \Big(\frac{1}{100}\Big)$ hours [Less distance, Less time]
Time taken to cover 350 km
= $\Big(\frac{1}{100} \times 350 \Big)$ hours
= $\Big(\frac{7}{2}\Big)$ hours
= $3\frac{1}{2}$ hours [More distance, More time]
Hence, option 3 is the correct option.
If the cost of 5 bars of soap is ₹85, what will be the cost of 1 dozen such bars?
1 dozen = 12 bars
Cost of 5 bars of soap = ₹ 85
Cost of 1 bar of soap = ₹ $\Big(\frac{85}{5}\Big)$ = ₹ 17 [Less bars, Less cost]
Cost of 12 bars of soap = ₹ (17 x 12) = ₹ 204 [More bars, More cost]
Hence, option 2 is the correct option.
If the cost of 6 note-books is ₹282, what is the cost of 8 such note-books?
Cost of 6 note-books = ₹ 282
Cost of 1 note-book = ₹ $\Big(\frac{282}{6}\Big)$ = ₹ 47 [Less note-books, Less cost]
Cost of 8 note-books = ₹ (47 x 8) = ₹ 376 [More note-books, More cost]
Hence, option 1 is the correct option.
If the cost of 16 oranges is ₹124, how many oranges can be bought for ₹155?
For ₹ 124, oranges bought = 16
For ₹ 1, oranges bought = $\Big(\frac{16}{124}\Big) = \Big(\frac{4}{31}\Big)$ [Less money, Less oranges]
For ₹ 155, oranges bought = $\Big(\frac{4}{31} \times 155 \Big)$ = (4 x 5) = 20 [More money, More oranges]
Hence, option 3 is the correct option.
If the cost of 20 packets of 8 pencils each is ₹400, what is the cost of 25 packets of 12 pencils each?
Number of pencils in 20 packets of 8 pencils each = (20 x 8) = 160
Number of pencils in 25 packets of 12 pencils each = (25 x 12) = 300
Now, cost of 160 pencils = ₹ 400
Cost of 1 pencil = ₹ $\Big(\frac{400}{160}\Big) = \Big(\frac{5}{2}\Big)$ [Less pencils, Less cost]
Cost of 300 pencils = ₹ $\Big(\frac{5}{2} \times 300 \Big)$ = ₹ (5 x 150) = ₹ 750 [More pencils, More cost]
Hence, option 2 is the correct option.
Fill in the blanks:
(i) Less is the number of articles, the ___________ will be their value.
(ii) The total cost vary ___________ as the number of articles bought.
(iii) A man saves ₹6000 in a year. His savings in 3 months is ₹ ___________
(iv) If the cost of 6 pens is ₹102, then the cost of 8 pens is ₹ ___________
(v) If a car consumes 6 litres of petrol in covering 111 km, then in 1 litre it covers ___________ km.
(i) Less is the number of articles, the less will be their value.
(ii) The total cost vary directly as the number of articles bought.
(iii) Savings in 12 months = ₹ 6000
Savings in 1 month = ₹ $\Big(\frac{6000}{12}\Big)$ = ₹ 500
Savings in 3 months = ₹ (500 x 3) = ₹ 1500
(iv) Cost of 6 pens = ₹ 102
Cost of 1 pen = ₹ $\Big(\frac{102}{6}\Big)$ = ₹ 17
Cost of 8 pens = ₹ (17 x 8) = ₹ 136
(v) In 6 litres, the car covers = 111 km
In 1 litre, the car covers = $\Big(\frac{111}{6}\Big)$ km = 18.5 km
Write (T) for true and (F) for false for each of the following statements:
(i) More is the number of articles, more will be their value. ___________
(ii) More men at work, more is the work done. ___________
(iii) More men at work, less will be the time taken to finish a piece of work. ___________
(iv) If 5 men can finish a work in 15 days, then 1 man can finish it in 3 days. ___________
(v) More is the speed of a car, more will be the time taken to cover a fixed distance. ___________
(i) T
Cost of articles is directly proportional to the number of articles.
(ii) T
Work done is directly proportional to the number of men at work.
(iii) T
More men at work will finish the work in less time.
(iv) F
Fewer men at work will take more time. So, 1 man can finish the work in (15 x 5) = 75 days, not 3 days.
(v) F
More is the speed of a car, less will be the time taken to cover a fixed distance.
Sajal went to the grocery store to purchase some vegetables. He bought 2.5 kg potatoes for ₹70; 4.5 kg onions for ₹135, 1.5 kg ladyfinger for ₹48 and 3 kg tomatoes at the rate of ₹29 per kg.
1. Cost of 3 kg tomatoes = ₹ (29 x 3) = ₹ 87
Total cost of vegetables = ₹ (70 + 135 + 48 + 87) = ₹ 340
Amount of money he got back = ₹ (500 − 340) = ₹ 160
Hence, option (b) is the correct option.
2. Cost of 2.5 kg potatoes = ₹ 70
Cost of 1 kg potatoes = ₹ $\Big(\frac{70}{2.5}\Big)$ = ₹ 28 [Less potatoes, Less cost]
Cost of 4 kg potatoes = ₹ (28 x 4) = ₹ 112 [More potatoes, More cost]
Hence, option (c) is the correct option.
3. Cost of 1.5 kg ladyfinger = ₹ 48
Cost of 1 kg ladyfinger = ₹ $\Big(\frac{48}{1.5}\Big)$ = ₹ 32 [Less ladyfinger, Less cost]
Cost of 2.5 kg ladyfinger = ₹ (32 x 2.5) = ₹ 80 [More ladyfinger, More cost]
Hence, option (a) is the correct option.
4. Cost of 1 kg potatoes = ₹ $\Big(\frac{70}{2.5}\Big)$ = ₹ 28
Cost of 3 kg potatoes = ₹ (28 x 3) = ₹ 84
Cost of 1 kg onions = ₹ $\Big(\frac{135}{4.5}\Big)$ = ₹ 30
Cost of 2 kg onions = ₹ (30 x 2) = ₹ 60
Cost of 1 kg tomatoes = ₹ 29
Cost of 4 kg tomatoes = ₹ (29 x 4) = ₹ 116
Total bill = ₹ (84 + 60 + 116) = ₹ 260
Hence, option (b) is the correct option.
Assertion (A): If the cost of 15 pens is ₹180, then the cost of 7 pens is ₹84.
Reason (R): For finding the values of a given number of units, we first find the value of 1 unit.
Cost of 15 pens = ₹ 180
Cost of 1 pen = ₹ $\Big(\frac{180}{15}\Big)$ = ₹ 12 [Less pens, Less cost]
Cost of 7 pens = ₹ (12 x 7) = ₹ 84 [More pens, More cost]
So, Assertion (A) is true.
For finding the values of a given number of units, we first find the value of 1 unit.
So, Reason (R) is true and is the correct explanation of Assertion (A), since the cost of 7 pens is found by first finding the cost of 1 pen.
Hence, option 1 is the correct option.
Assertion (A): If a car travels 252 km in 6 hours, then it will travel 200 km in 5 hours.
Reason (R): Distance travelled by a car is directly proportional to the time it runs.
In 6 hours, the car travels = 252 km
In 1 hour, the car travels = $\Big(\frac{252}{6}\Big)$ km = 42 km [Less time, Less distance]
In 5 hours, the car travels = (42 x 5) km = 210 km [More time, More distance]
Since 210 km ≠ 200 km, Assertion (A) is false.
Reason (R) is true, as distance travelled by a car is directly proportional to the time it runs.
Hence, option 4 is the correct option.
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