Question 1

If 20 articles cost ₹ 90, then the cost of 9 articles is?

Accepted Answer

Cost of 20 articles = ₹ 90 Cost of 1 article = ₹ 90/20 ∴ Cost of 9 article = 9 x 90/20 = ₹ 40.50

Question 2

If cost of 24 oranges is ₹ 72, then find out the cost of 120 oranges.

Accepted Answer

Let the required cost be ₹ N. More orange, more cost (Direct proportion) 24 : 120 : : 72 : N ∴ N = (120 x 72)/24 = ₹ 360

Question 3

If cost of 12 pens is ₹ 84, then what is the cost of 10 such pens?

Accepted Answer

∵ Cost of 12 pens = ₹ 84 Cost of 1 pen = ₹ 84/12 ∴ Cost of 10 pens = (84/12) x 10 = 7 x 10 = ₹ 70

Question 4

If cost of 15 eggs is ₹ 75, then find out the cost of 4 dozens eggs.

Accepted Answer

∵ Cost of 15 eggs = ₹ 75 ∴ Cost of 1 egg = ₹ 75/15 ∴ Cost of 4 dozens (4 x 12) = Cost of 48 eggs = (75/15) x 48 = ₹ 240

Question 5

If 16 dozens bananas cost ₹ 360, then how many bananas can be bought in ₹ 60?

Accepted Answer

Let the required number of bananas be N. 16 dozens bananas = 16 x 12 = 192 bananas Less bananas, Less cost (Direct proportion) 360 : 60 : : 192 : N ∴ N = (60 x 192)/360 = 32 bananas

Question 6

A worker makes a toy in every 2h. If he works for 80h, then how many toys will he make?

Accepted Answer

Let number of toys be N. More hours, More toys (Direct proportion) 2 : 80 : : 1 : N ⇒ N = 80/2 = 40 toys

Question 7

If 45 m of a uniform rod weight 171 kg, then what will be the weight of 12 m of the same rod?

Accepted Answer

Let the required weight be w kg. Less length, Less weight (Direct proportion) 45 : 12 :: 171 : w ∴ w = (12 x 171)/45 = 45.6 kg

Question 8

In a race , Ravi covers 5 km in 20 min. How much distance will he cover in 100 min?

Accepted Answer

∵ Distance covered in 20 min = 5 km ∴ Distance covered in 1 min = 5/20 km ∴ Distance covered in 100 min = (5/20) x 100 = 5 x 5 = 25 km

Question 9

A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole?

Accepted Answer

∵ 8 m shadow means original height = 12 m ∴ 1 m shadow means original height = 12/8 m ∴ 100 m shadow means original height = (12/8) x 100 m = (6/4) x 100 = 6 x 25 = 150 m

Question 10

If the cost of x meters of wire is 'd' rupees, that find the cost (in Rupees) of 'y' meters of wire at the same rate.

Accepted Answer

Cost of x meters ropes = Rs. d ∴ Cost of 1 meters ropes = Rs. d /x ∴ Cost of y meters ropes = Rs. dy/x

Question 11

In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

Accepted Answer

40 cows eat 40 bags of husk in 40 days. ∴ 1 cows eat 40 bags of husk in 40 x 40 days. ∴ 1 cows eat 1 bags of husk in 40 x 40 / 40 days. ∴ 1 cows eat 1 bags of husk in 40 days.

Question 12

21 goats eat as much as 15 cows. How many goats eat as much as 35 cows?

Accepted Answer

15 Cows eat as much as 21 Goats. ∴ 1 Cows eat as much as 21/ 15 Goats. ∴ 35 Cows eat as much as 21 x 35 / 15 Goats. ∴ 35 Cows eat as much as 21 x 7 / 3 Goats. ∴ 35 Cows eat as much as 7 x 7 Goats. ∴ 35 Cows eat as much as 49 Goats.

Question 13

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

Accepted Answer

Since 39 persons can repair a road by working 5 hours in a day in 12 days. ∴ 1 persons can repair a road by working 5 hours in a day in 39 x 12 days. ∴ 1 persons can repair a road by working 1 hours in a day in 39 x 12 x 5 days. ∴ 30 persons can repair a road by working 1 hours in a day in 39 x 12 x 5 / 30 days. ∴ 30 persons can repair a road by working 6 hours in a day in 39 x 12 x 5 / 30 x 6 days. ∴ 30 persons can repair a road by working 6 hours in a day in 39 x 2 x 1 / 6 days. ∴ 30 persons can repair a road by working 6 hours in a day in 39 x 1 x 1 / 3 days. ∴ 30 persons can repair a road by working 6 hours in a day in 13 days.

Question 14

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

Accepted Answer

4 mat-weavers in 4 days can weave 4 mats. 1 mat-weavers in 4 days can weave 4 / 4 mats. 1 mat-weavers in 1 days can weave 4 / 4 x 4 mats. 8 mat-weavers in 1 days can weave 4 x 8 / 4 x 4 mats. 8 mat-weavers in 8 days can weave 4 x 8 x 8 / 4 x 4 mats. 8 mat-weavers in 8 days can weave 4 x 2 x 2 mats. 8 mat-weavers in 8 days can weave 16 mats.

Question 15

If a quarter Kg of potato costs 60 paise, How many paise will 200 gm cost?

Accepted Answer

As we know that Quarter Kg = 250 Gram According to question, 250 Gram of potato costs 60 paise. ∴ 1 Gram of potato costs 60 / 250 paise. ∴ 200 Gram of potato costs 60 x 200 / 250 paise. ∴ 200 Gram of potato costs 60 x 20 / 25 paise. ∴ 200 Gram of potato costs 60 x 4 / 5 paise. ∴ 200 Gram of potato costs 12 x 4 paise. ∴ 200 Gram of potato costs 48 paise.

Question 16

In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

Accepted Answer

According to question, 40 cows eat 40 bags of husk in 40 days. 1 cows eat 40 bags of husk in 40 x 40 days. 1 cows eat 1 bags of husk in 40 x 40 / 40 days. 1 cows eat 1 bags of husk in 40 days.

Question 17

An industrial loom weaves 0.128 meters of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 meter of cloth?

Accepted Answer

According to given question, Since an industrial loom weaves 0.128 meters of cloth in 1 seconds. ∴ an industrial loom weaves 1 meters of cloth in 1 / 0.128 seconds. ∴ an industrial loom weaves 25 meters of cloth in 1 x 25 / 0.128 seconds. ∴ an industrial loom weaves 25 meters of cloth in 25 / 0.128 seconds. ∴ an industrial loom weaves 25 meters of cloth in 195 seconds.

Question 18

If 8 men can reap 80 hectares in 24 days, then how many hectares can 36 men reap in 30 days?

Accepted Answer

Since 8 men in 24 days can reap 80 hectares. ∴ 1 men in 24 days can reap 80 / 8 hectares. ∴ 1 men in 1 days can reap 80 / 8 x 24 hectares. ∴ 36 men in 1 days can reap 80 x 36 / 8 x 24 hectares. ∴ 36 men in 30 days can reap 80 x 36 x 30 / 8 x 24 hectares. ∴ 36 men in 30 days can reap 10 x 36 x 30 / 24 hectares. ∴ 36 men in 30 days can reap 10 x 3 x 30 / 2 hectares. ∴ 36 men in 30 days can reap 10 x 3 x 15 hectares. ∴ 36 men in 30 days can reap 450 hectares.

Question 19

If the cost of x meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?

Accepted Answer

Question 20

If the price of 23 toys is Rs. 276, then what will the price (Rs.) of 12 toys?

Accepted Answer

Unitary Method Questions