Exercise 10.1

1. The cost of 5 meters of a particular quality of cloth is ₹210. Find the cost of (i) 2 (ii) 4 (iii) 10 (iv) 13 meters of cloth of the same quality.

Solution:

Cost of 1 meter of cloth = ₹210/5 = ₹

(i) Cost of 2 meters = × ₹ 42 = ₹

(ii) Cost of 4 meters = × ₹ 42 = ₹

(iii) Cost of 10 meters = × ₹ 42 = ₹

(iv) Cost of 13 meters = × ₹ 42 = ₹

2. Fill the table.

Solution:

Cost of 1 apple = ₹

3. 48 bags of paddy costs ₹16,800 then find the cost of 36 bags of paddy.

Solution:

Cost of 1 bag of paddy = ₹ 1648 = ₹

Cost of 36 bags of paddy = × ₹ 350 = ₹

4. Monthly average expenditure of a family with 4 members is ₹2,800. Find the monthly average expenditure of a family with only 3 members.

Solution:

Monthly average expenditure of a family of 4 member =

Monthly average expenditure of a family of 1 member = 28004 =

Monthly average expenditure of a family of 3 member = 700 × =

5. In a ship of length 28 m, height of its mast is 12 m. If the height of the mast in its model is 9 cm what is the length of the model ship?

Solution:

Let's assume the length of the model ship is x cm.

Ratio of height of mast to length of ship = 12/28 =

Height of mast in modelLength of model ship = 9/x cm = 3/7

x = ( × )/ = cm.

The length of the model ship is 21 cm.

6. A vertical pole of 5.6 m height casts a shadow 3.2 m long. At the same time find (i) the length of the shadow cast by another pole 10.5 m high (ii) the height of a pole which casts a shadow 5m long.

Solution:

Ratio of height to shadow = 5.63.2 =

(i) Shadow of 10.5 m pole = 10.51.75 = m

(ii) Height of pole with 5m shadow = × 5 = m

7. A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?

Solution:

Speed of the truck = 14km25minutes = (14 × )/25 kmhr = kmhr

Distance traveled in 5 hours = 33.6 km/hr × hours = km

8. If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 16 23 kilograms?

Solution:

Weight of 1 sheet = 4012 grams = grams

16 23 kg = kg = 503 × grams = grams

Number of sheets = 500003103 = 5000010 =

9. A train moves at a constant speed of 75 km/hr. (i) How far will it travel in 20 minutes? (ii) Find the time required to cover a distance of 250 km.

Solution:

(i) Distance = Speed × Time = km/hr × 20606020 hr = km

(ii) Time = DistanceSpeed = 250km75kmhr = hours = hours minutes

10. The design of a microchip has the scale 40:1. The length of the design is 18cm, find the actual length of the micro chip?

Solution:

Actual length = Design lengthScale factorScale factorDesign length = = cm or mm

11. The average age of doctors and lawyers together is 40. If the doctors average age is 35 and the lawyers average age is 50, find the ratio of the number of doctors to the number of lawyers.

Solution:

Let 'd' be the number of doctors and 'l' be the number of lawyers.

Total age of doctors =

Total age of lawyers =

Total age of doctors and lawyers = 40(d+l)35(ld)

35d + 50l = 40d + 40l

l = d

dl = 105 =

The ratio of doctors to lawyers is .