A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

Correct Answer: 7

Explanation:

Let the required number days be x.

Less spiders, More days (Indirect Proportion)

Less webs, Less days (Direct Proportion)

  S p i d e r s 1 : 7 W e b s 7 : 1 ? ? 7 : x 

=> 1 * 7 * x = 7 * 1 * 7 

=> x= 7

Correct Answer: 21 days

Explanation:

(2 x 14) men +(7 x 14) boys = (3 x 11) men + (8 x 11) boys

 =>5 men= 10 boys    => 1man= 2 boys

 Therefore, (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys

 

( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.

 Let the required  number of days be x.

 More boys , Less days     (Indirect proportion)

 More work , More days    (Direct proportion)

  B o y s 22 : 11 W o r k 1 : 3 ? ? 14 : x

 Therefore, (22 * 1 * x) = (11 * 3 * 14)

=> x = 21 

Hence, the required number of days = 21

Correct Answer: 60

Explanation:

Let the required no of hours be x. Then

 

Less men , More hours    (Indirct Proportion)

 

Therefore,  15:36 ::25:x 

=> (15 x X)=(36 x 25)  => x = 60

 

Hence, 15 men can do it in 60 hours.

Correct Answer: 110

Explanation:

Originally let there be x men.

Less men, More days     (Indirect Proportion)

 Therefore, (x-10) : x  :: 100 :110

=> (x - 10) * 110 = x * 100    => x= 110

Correct Answer: 49

Explanation:

Let the required length be x meters

 More men, More length built     (Direct proportion) 

Less days, Less length built      (Direct Proportion)

M e n 20 : 35 D a y s 6 : 3 ? ? 56 : x 

=> (20 x 6 x X)=(35 x 3 x 56) 

=> x = 49 

Hence, the required length is 49 m.

Correct Answer: 13

Explanation:

Let the required number of days be x.

Less persons, More days (Indirect Proportion)

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

P e r s o n s 30 : 39 W o r k i n g h o u r s / d a y 6 : 5 ? ? 12 : x

 

=> 30 * 6 * x = 39 * 5 * 12 

 

=> x= 13

Correct Answer: 12

Explanation:

Let the required no of working hours per day be x.

More pumps , Less working hours per day  (Indirect Proportion)

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

  P u m p s 4 : 3 D a y s 1 : 2 ? ? 8 : x

=> (4 * 1 * x) = (3 * 2 * 8)

=> x=12

Correct Answer: 11

Explanation:

Let the required no of binders be X.

Less books , Less binders       (Direct Proportion)

More days, Less binders         (Indirect proportion)

 

  B o o k s 900 : 660 D a y s 12 : 10 ? ? 18 : x

Therefore, (900 * 12 * x) =  (660 * 10 * 18)  

=> x = 11

Correct Answer: 24 days

Explanation:

Less Men, means more Days {Indirect Proportion}

Let the number of days be x then,

27 : 36 :: 18 : x

[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]                                

=>27x = 36 * 18

=> x = 24

 So 24 days will be required to get work done by 27 men.

Correct Answer: 48 paise

Explanation:

Quarter of Kg means 250 gm

Less weight, less price (Direct Proportion)

So,

250 : 200 :: 60 : x => x = 48

So 200 gm will cost 48 paise.