#### Exercise 10.1

Q1. 20 chocolates cost Rs 320. Find the cost of 35 such chocolates.

Solution:

Cost of 20 chocolates = Rs 320

Cost of 1 chocolate = Rs (\(\frac{320}{20}\)

Therefore, the cost of 35 chocolates = Rs (\(\frac{320}{20}\times 35\)

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Q2. The cost of 40 meters of cloth is Rs 200. Find the cost of 50 meters of cloth.

Solution:

Cost of 40 meters of cloth = Rs 200

Cost of 1 meter of cloth = Rs (\(\frac{200}{40}\)

Therefore, the cost of 50 chocolates = Rs (\(\frac{200}{40}\times 50\)

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Q3. A car can cover a distance of 522 km on 36 liters of petrol. How far can it travel on 14 litres of petrol?

Solution:

Number of kilometers a car can cover by using 36 liters = 522 km

Number of kilometers a car can cover by using 1 liter = \(\frac{522}{36}\)

Hence, the number of kilometers a car can cover by using 14 liters = (\(\frac{522}{36} \times\)

Q4. Travelling 900 km by rail costs Rs 280. What would be the fare for a journey of 360 km when a person travels by the same class?

Solution:

Cost of travelling 900 km by rail = Rs 280

Cost of travelling 1 km by rail = Rs (\(\frac{280}{900}\)

Hence, Cost of travelling 360 km by rail = Rs \(\frac{280}{900}\times 360\)

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Q5. If 6 oil tankers can be filled by a pipe in \(4\frac{1}{2}\)

Solution:

Time taken by 6 oil tankers to be filled by a pipe = \(4 \frac{1}{2} \; hours \; = \frac{9}{2} \; hours\)

Time taken by 1 oil tankers to be filled by a pipe = \(\frac{\frac{9}{2}}{6}\)

Hence, the time taken by 4 oil tankers to be filled by a pipe = \(\frac{9}{12}\times 4\)

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Q6. \(\frac{3}{4}\)

Solution:

Let the salary be â€˜xâ€™

Given,

\(\frac{3}{4}\)

- \(\frac{3}{4}\times x\)
= Rs 600 - x = Rs \(600 \times \frac{4}{3}\)
- x = Rs 800

Therefore, the salary per month is Rs 800

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Q7. The cost of 32 tables is Rs 23520. Find the number of such tables that can be purchased for Rs 51450

Solution:

Number of tables bought for Rs 23520 = 32

Number of tables bought for Re 1 = \(\frac{32}{23520}\)

Number of tables bought for Rs 51450 = \(\frac{32}{23520} \times 51450\)

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Q8. The yield of wheat from 6 hectares is 280 quintals. Find the number of hectares required for a yield of 225 quintals.

Solution:

Number of hectares required for a yield of 280 quintals = 6 hectares

Number of hectares required for a yield of 1 quintal = \(\frac{6}{280}\)

Hence, the number of hectares required for a yield of 225 quintals = \(\frac{6}{280} \times 225\)

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Q9. Fifteen post cards cost Rs 2.25. What will be the cost of 36 post cards? How many postcards can we buy in Rs 45?

Solution:

Cost of 15 post cards = Rs 2.25

Cost of 1 post card = Rs \(\frac{2.25}{15}\)

Cost of 36 post cards = Rs \(\frac{2.25}{15}\times 36\)

As we know,

Number of postcards bought at Rs 2.25 = 15

Number of postcards bought at Re 1 = \(\frac{15}{2.25}\)

Number of postcards bought at Rs 45 = \(\frac{15}{2.25} \times 45\)

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Q10. A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost?

Solution:

Cost of a rail journey of 75 km = Rs 215

Cost of a rail journey of 1 km = Rs \(\frac{215}{75}\)

Cost of a rail journey of 120 km = Rs \(\frac{215}{75} \times 120\)

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Q11. If the sales tax on a purchase worth Rs 60 is Rs 4.20. What will be the sales tax on the purchase worth of Rs 150?

Solution:

Sales tax on the purchase worth of Rs 60 = Rs 4.20

Sales tax on the purchase worth of Re 1 = Rs \(\frac{4.20}{60}\)

Sales tax on the purchase worth of Rs 150 = Rs \(\frac{4.20}{60} \times 150\)

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Q12. 52 packets of 12 pencils each, cost Rs 499.20. Find the cost of 65 packets

of 10 pencils each.

Solution:

Total number of pencils in 52 packets of 12 pencils each = 52 x 12 = 624

Cost of 624 pencils = Rs 499.20

Cost of 1 pencil = Rs \(\frac{499.20}{624}\)

Now,

Number of pencils in 65 packets of 10 pencils each = 65 x 10 = 650 pencils

Therefore, cost of 650 pencils = Rs \(\frac{499.20}{624} \times 650\)