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Question 1

Q6. If 12 carpenters, working 6 hours a day, can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day ?

1260

1320

920

1380

Answer

Answer : 1380

Let the required number of chairs be x . Then ,

More carpenters, More chairs	(Direct Proportion)
More hours per day, More chairs	(Direct Proportion)
More days, More chairs	(Direct Proportion)

∴ 12 × 6 × 24 × x = 18 × 8 × 36 × 460
⇒ x = (18 × 8 × 36 × 460)/(12 × 6 × 24) = 1380

Hence, the required number of chairs is 1380.

⚔ DISCUSS

Question 2

Q7. If 9 examiners can examine a certain number of answer books in 12 days, working 5 hours a day; for how many hours a day would 4 examiners have to work in order to examine twice the number of answer books in 30 days ?

6

8

9

10

Answer

Answer : 9

Let the required number of working hours per day be x . Then ,

Less examiners, More working hours per day	(Indirect Proportion)
More days, Less working hours per day	(Indirect Proportion)
More answer books, More working hours per day	(Direct Proportion)

∴ 4 × 30 × 1 × x = 9 × 12 × 2 × 5
⇒ x = (1080)/(120) = 9

Hence, the required number of working hours per day is 9 hours.

⚔ DISCUSS

Question 3

Q8. 400 persons, working 9 hours per day complete ¹⁄₄^th of the work in 10 days. The number of additional persons, working 8 hours per day, required to complete the remaining work in 20 days, is :

675

275

250

825

Answer

Answer : 275

Let the required number of persons completing the work in 20 days be x . Then ,
Work done = 1/4, Remaining work = 1 - (1/4) = 3/4

More work, More men required	(Direct Proportion)
More days, Less men required	(Indirect Proportion)
Less hours per day, More men required	(Indirect Proportion)

∴ (1/4) × 20 × 8 × x = (3/4) × 10 × 9 × 400
⇒ x = 27000/40 = 675

Hence, Additional men = 675 - 400 = 275.

⚔ DISCUSS

Question 4

Q9. A certain number of persons can dig a trench 100 m long, 50 m broad and 10 m deep in 10 days. The same number of persons can dig another trench 20 m broad and 15 m deep in 30 days. The length of the second trench is :

400 m

500 m

800 m

900 m

Answer

Answer : 500 m

Let the required length be x metres. Then ,

More breadth, less length	(Inirect Proportion)
More depth, less length	(Indirect Proportion)
More days, More length	(Direct Proportion)

∴ 20 × 15 × 10 × x = 50 × 10 × 30 × 100
⇒ x = 1500/3 = 500

Hence, the required length is 500 metres.

⚔ DISCUSS

Question 5

Q10. 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?

10

13

14

15

Answer

Answer : 13

Let the required number of days be x. Then ,

Less persons, More days	(Inirect Proportion)
More working hours per day, Less days	(Indirect Proportion)

∴ 30 × 6 × x = 39 × 5 × 12
⇒ x = (39 × 5 × 12)/(30 × 6) = 13

Hence, the required number of days is 13.

⚔ DISCUSS

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