13-07-2021 Answers

 1. If 27 kg of corn would feed 42 horses for 21 days, in how many days would 36 kg of it feed 21 horses?

Answer: 56 days

Solution: Let the number of days to complete the work be x.

More kgs more days ~ Direct proportion.

More horses more days ~ Indirect proportion.

x*27*21 = 21*36*42; x = 56

2. A tree 6m tall casts a 4m long shadow. At the same time, a flagpole casts a 50m long shadow. How long is the flagpole?

Answer: 75m 

Solution: Let the length of the flagpole be a.

6:4 = a:50; a=50*6/4 = 75

3. Four trucks carrying 4 tons each can move 128 tons in 8 days. In how many days will 6 trucks carrying 3 tons each move 540 tons?

Answer: 30 days

Solution: Let no of days required be x.

More lorries less days ~ Indirect proportion.

More capacity less days ~ Indirect proportion.

More weight more days ~ Direct proportion.

x*6*3*128 = 4*4*540*8; x = 30

4. If 21 cows eat that much as 15 buffaloes, how many cows will eat that much as 35 buffaloes ?

Answer: 49

Solution: Let the amount a cow eats be c and the buffalo eats be b.

21c=15b, c=5b/7.

Let x number of cows eat as much as 35 buffaloes.

x * 5b/7 = 35b; Solving x = 49.

5. 16 men can reap a field in 30 days. In how many days will 20 men reap the field ?

Answer: 24 days

Solution: Let the no of days required be x.

More men less days ~ Indirect proportion

x*20 = 16*30; x = 24

6. The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozens of such mangoes?

Answer: Rs.2500

Solution: 357:1517.25 = 49*12:x

x = (1517.25*49*12)/357 = 2499 which is ~ 2500

7. Running at the same constant rate, 6 identical machines can produce a total of 270 cans per minute. At this rate, how many cans could 10 such machines produce in 4 minutes?

Answer: 1800

Solution: Let the number of cans produced be x.

More machines more cans ~ Direct proportion

More minutes more cans ~ Direct proportion

x*6*1 = 270*10*4; x = 1800

8. If 17 labourers can dig a ditch 26 metres long in 18 days working 8 hours a day. How many labourers should be engaged to dig a similar ditch 39 metres long in 6 days, each labourer working 9 hours a day?

Answer: 68

Solution: Let the no of labourers to be engaged be a.

More length more labourers ~ Direct proportion.

More days less labourer ~ Indirect proportion.

More hours less labourer ~ Indirect proportion.

a*26*6*9 = 17*39*18*8; a = 68

9. If 3 persons weave 336 shawls in 14 days, how many shawls will 8 persons weave in 5 days?

Answer: 320

Solution: Let the number of shawls that can be weaved be x.

More persons more shawls ~ Direct proportion.

More days more shawls ~ Direct proportion.

So 336*8*5 = x*3*14,x = 320

10. If 5 men working 6 hours a day can reap a field in 20 days. In how many days will 15 men reap the field, working 8 hours a day?

Answer: 5 days

Solution: Let the no of days required be x.

More men less days - Indirect proportion

More hours less days - Indirect proportion

x*15*8 = 5*6*20; x = 5

11.8 men can finish a piece of work in 40 days. If 2 more men join with them, then the work will be completed in

Answer: 32 days

Solution: Let the number of days to complete the work be a.

More persons less days - InDirect proportion.

8*40 = (8+2)*a; a=32 

12.If 80 lamps can be lighted 5 hours per day for 10 days for Rs.21.25, then the number of lamps which can be lighted 4 hours daily for 30 days for Rs.76.50, is

Answer: 120

Solution: Let the no of lamps be a.

More money - more lamps ~ Direct proportion.

More lamps - less hours and days ~ Indirect proportion.

a*4*30*21.25 = 80*5*10*76.50; a = 120

13.Thousand people in a camp have provisions for 22 days. How long will the provision last if 100 more join them?

Answer: 20 days

Solution: Let the consumption/person be a.

Quantity of provision = 1000*22*a = 22000a

No of days when 100 more join = 22000a/(1100*a) = 20

14.A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

Answer: 110

Solution: Let the number of men be a.

More men less days - Indirect proportion.

a*100 = (a-10)*110; a = 110

15. If 22.5 metres of a uniform iron rod weighs 85.5 kg. What will be the weight of 6 metres of the same rod ?

Answer: 22.8 kg

Solution: Let, weight of the desired rod be a kgs.

More length more weight - Direct proportion.

a * 22.5 = 85.5 * 6; a = 22.8