Unitary Method — Exercise 9(A)

The cost of 11 pens is ₹253. Find:

(i) the cost of 1 pen.

(ii) the cost of 24 pens.

Answer

By the unitary method, we have:

Cost of 11 pens = ₹ 253

(i) Cost of 1 pen = ₹ $\Big(\dfrac{253}{11}\Big)$ = ₹ 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?

Answer

By the unitary method, we have:

Oil contained in 14 tins = 210 litres

(i) Oil contained in 1 tin = $\Big(\dfrac{210}{14}\Big)$ 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?

Answer

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 = $\Big(\dfrac{192}{16}\Big)$ 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?

Answer

Cost of 8 kg of rice = ₹ 620

Cost of 1 kg of rice = ₹ $\Big(\dfrac{620}{8}\Big)$ [Less rice, Less cost]

Cost of 18 kg of rice = ₹ $\Big(\dfrac{620}{8} \times 18 \Big)$ = ₹ 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?

Answer

Cost of 13 m of cloth = ₹ 1664

Cost of 1 m of cloth = ₹ $\Big(\dfrac{1664}{13}\Big)$ = ₹ 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?

Answer

Oil contained in 15 tins = 235 l

Oil contained in 1 tin = $\Big(\dfrac{235}{15}\Big) \text{ l }= \Big(\dfrac{47}{3}\Big)$ l [Less tins, Less oil]

Oil contained in 12 tins = $\Big(\dfrac{47}{3} \times 12 \Big)$ 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?

Answer

Weight of 6 m of the rod = 21 kg

Weight of 1 m of the rod = $\Big(\dfrac{21}{6}\Big) \text{ kg }= \Big(\dfrac{7}{2}\Big)$ kg [Less length, Less weight]

Weight of 20 m of the rod = $\Big(\dfrac{7}{2} \times 20 \Big)$ 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?

Answer

Number of books weighing 28 kg = 63

Number of books weighing 1 kg = $\Big(\dfrac{63}{28}\Big) = \Big(\dfrac{9}{4}\Big)$ [Less weight, Less books]

Number of books weighing 60 kg = $\Big(\dfrac{9}{4} \times 60 \Big)$ = (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?

Answer

For ₹ 95, bananas bought = 25

For ₹ 1, bananas bought = $\Big(\dfrac{25}{95}\Big) = \Big(\dfrac{5}{19}\Big)$ [Less money, Less bananas]

For ₹ 152, bananas bought = $\Big(\dfrac{5}{19} \times 152 \Big)$ = (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?

Answer

Number of boxes needed for 1080 pens = 15

Number of boxes needed for 1 pen = $\Big(\dfrac{15}{1080}\Big) = \Big(\dfrac{1}{72}\Big)$ [Less pens, Less boxes]

Number of boxes needed for 1800 pens = $\Big(\dfrac{1}{72} \times 1800 \Big)$ = 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?

Answer

Time taken to travel 204 km = 9 hours

Time taken to travel 1 km = $\Big(\dfrac{9}{204}\Big) \text{ hours }= \Big(\dfrac{3}{68}\Big)$ hours [Less distance, Less time]

Time taken to travel 340 km = $\Big(\dfrac{3}{68} \times 340 \Big)$ 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?

Answer

In covering 65 km, diesel consumed = 12.5 litres

In covering 1 km, diesel consumed = $\Big(\dfrac{12.5}{65}\Big)$ litres [Less distance, Less diesel]

In covering 416 km, diesel consumed = $\Big(\dfrac{12.5}{65} \times 416 \Big) \text{ litres }= \Big(\dfrac{5200}{65}\Big)$ 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?

Answer

For 20 shirts, cloth required = 44 m

For 1 shirt, cloth required = $\Big(\dfrac{44}{20}\Big) \text{ m }= \Big(\dfrac{11}{5}\Big)$ m [Less shirts, Less cloth]

For 35 shirts, cloth required = $\Big(\dfrac{11}{5} \times 35 \Big)$ 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?

Answer

Weight of 18 bags = 297 kg

Weight of 1 bag = $\Big(\dfrac{297}{18}\Big) \text{ kg }= \Big(\dfrac{33}{2}\Big)$ kg [Less bags, Less weight]

Weight of 22 bags = $\Big(\dfrac{33}{2} \times 22 \Big)$ 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?

Answer

Time taken to walk 14 km = 5 hours

Time taken to walk 1 km = $\Big(\dfrac{5}{14}\Big)$ hours [Less distance, Less time]

Time taken to walk 22.4 km = $\Big(\dfrac{5}{14} \times 22.4 \Big) \text{ hours }= \Big(\dfrac{112}{14}\Big)$ hours = 8 hours [More distance, More time]

Hence, the man would take 8 hours to walk 22.4 km.