Ratio & Proportion — Exercise 9(C)

The price of 25 identical articles is ₹ 1,750. Find the price of 13 articles.

Answer

Given,

Price of 25 articles = ₹ 1,750

Price of 1 article = $\dfrac{1750}{25}$ = ₹ 70.

Price of 13 articles = 13 × ₹ 70 = ₹ 910.

Hence, the price of 13 articles is ₹ 910.

A motorbike travels 330 km consuming 5 litres of petrol. How much distance will it cover consuming 2.5 litres of petrol?

Answer

Given,

Distance covered in 5 litres = 330 km

Distance covered in 1 litre = $\dfrac{330}{5}$ = 66 km.

Distance covered in 2.5 litres = 2.5 × 66 = 165 km.

Hence, the motorbike will cover 165 km consuming 2.5 litres of petrol.

The cost of 35 envelopes is ₹ 105. How many envelopes can be bought for ₹ 90?

Answer

Given,

Cost of 35 envelopes = ₹ 105

Number of envelopes bought for ₹ 105 = 35

Number of envelopes bought for ₹ 1 = $\dfrac{35}{105}$ envelopes.

Number of envelopes bought for ₹ 90 = $\dfrac{35}{105} \times 90$

= $\dfrac{1}{3} \times 90$

= 30 envelopes.

Hence, 30 envelopes can be bought for ₹ 90.

The cost of 10 kg of wheat is ₹ 180;

(i) what will 18 kg of wheat cost?

(ii) what quantity of wheat can be purchased for ₹ 432?

Answer

Given,

Cost of 10 kg of wheat = ₹ 180

Cost of 1 kg of wheat = $\dfrac{180}{10}$ = ₹ 18.

(i) Cost of 18 kg of wheat = 18 × ₹ 18 = ₹ 324.

Hence, 18 kg of wheat costs ₹ 324.

(ii) Quantity of wheat purchased for ₹ 18 = 1 kg

Quantity of wheat purchased for ₹ 432 = $\dfrac{432}{18}$ = 24 kg.

Hence, 24 kg of wheat can be purchased for ₹ 432.

A tree 24 m high casts a shadow of 15 m. At the same time, another tree casts a shadow of 6 m. Find the height of the second tree.

Answer

Given,

Height of the first tree = 24 m, shadow of the first tree = 15 m

Shadow of the second tree = 6 m

For a shadow of 15 m, the height = 24 m

For a shadow of 1 m, the height = $\dfrac{24}{15}$ m.

For a shadow of 6 m, the height = $\dfrac{24}{15} \times 6$

= $\dfrac{144}{15}$

= 9.6 m

Hence, the height of the second tree is 9.6 m.

A loaded truck travels 18 km in 25 minutes. If the speed remains the same, how far will it travel in 2 hours?

Answer

Given,

Distance travelled in 25 minutes = 18 km

2 hours = 2 × 60 minutes = 120 minutes

Distance travelled in 1 minute = $\dfrac{18}{25}$ km.

Distance travelled in 120 minutes = $\dfrac{18}{25} \times 120$

= $\dfrac{2160}{25}$

= 86.4 km.

Hence, the truck will travel 86.4 km in 2 hours.

Jai Singh and Vijay Singh start a business by investing ₹ 6,00,000 and ₹ 9,00,000 respectively. At the end of the year, they earn a profit of ₹ 1,50,000. What is the share of Vijay Singh out of this profit?

Answer

Given,

Jai Singh's investment = ₹ 6,00,000

Vijay Singh's investment = ₹ 9,00,000

Total profit = ₹ 1,50,000

Ratio of investments = 600000 : 900000 = 6 : 9 = 2 : 3

Let the shares of Jai Singh and Vijay Singh be 2x and 3x respectively.

⇒ 2x + 3x = 150000

⇒ 5x = 150000

⇒ x = $\dfrac{150000}{5}$

⇒ x = ₹ 30,000

Vijay Singh's share = 3x = 3 × ₹ 30,000 = ₹ 90,000.

Hence, the share of Vijay Singh is ₹ 90,000.

Out of 350 students, 150 are girls. Find the ratio of :

(i) number of girls to the total number of students.

(ii) number of boys to the number of girls.

Answer

Given,

Total students = 350

Number of girls = 150

Number of boys = 350 − 150 = 200

(i) Ratio of girls to total students = 150 : 350

H.C.F. of 150 and 350 is 50.

$\dfrac{150 \div 50}{350 \div 50} = \dfrac{3}{7} = 3 : 7$

Hence, the ratio of girls to the total number of students is 3 : 7.

(ii) Ratio of boys to girls = 200 : 150

H.C.F. of 200 and 150 is 50.

$\dfrac{200 \div 50}{150 \div 50} = \dfrac{4}{3} = 4 : 3$

Hence, the ratio of boys to girls is 4 : 3.

If the cost of one dozen identical articles is ₹ 166. What is the cost of 36 such articles?

Answer

Given,

Cost of one dozen (12) articles = ₹ 166

36 articles = 3 dozens

Cost of 36 articles = 3 × ₹ 166 = ₹ 498.

Hence, the cost of 36 articles is ₹ 498.

A car moves with a uniform speed and covers 180 km in 3 hours.

(i) In how much time will it cover 240 km?

(ii) How much distance will it cover in 2 hours?

Answer

Given,

Distance covered in 3 hours = 180 km

Speed of the car = $\dfrac{180}{3}$ = 60 km/h.

(i) Time taken to cover 240 km = $\dfrac{240}{60}$ = 4 hours.

Hence, the car will cover 240 km in 4 hours.

(ii) Distance covered in 2 hours = 60 × 2 = 120 km.

Hence, the car will cover 120 km in 2 hours.