# Chain Rule Questions

Q:

2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in

 A) 18 days B) 21 days C) 24 days D) 30 days

Answer & Explanation Answer: B) 21 days

Explanation:

$\inline&space;\fn_jvn&space;(2\times&space;14)&space;men&space;+(7\times&space;14)boys=(3\times&space;11)men+(8\times&space;11)boys$

$\inline&space;\fn_jvn&space;\Leftrightarrow$  5 men= 10 boys  $\inline&space;\fn_jvn&space;\Leftrightarrow$  1man= 2 boys

$\inline&space;\fn_jvn&space;\therefore$  (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)

$\inline&space;\fn_jvn&space;\left.\begin{matrix}&space;Boys\:&space;22:11\\&space;Work\:&space;1:3&space;\end{matrix}\right\}::14:x$

$\inline&space;\fn_jvn&space;\therefore&space;\:&space;\:&space;(22\times&space;1\times&space;x)=(11\times&space;3\times&space;14)$   $\inline&space;\fn_jvn&space;\Leftrightarrow$  $\inline&space;\fn_jvn&space;x=&space;\frac{462}{22}=21$

Hence, the required number of days = 21

13 6845
Q:

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

 A) 9 B) 10 C) 11 D) 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)

$\inline&space;\fn_jvn&space;\left.\begin{matrix}&space;pumps\:&space;4:3\\&space;Days\;&space;\;&space;\;&space;\;&space;1:2&space;\end{matrix}\right\}::8:x$

$\inline&space;\fn_jvn&space;\therefore$  $\inline&space;\fn_jvn&space;4\times&space;1\times&space;x=&space;3\times&space;2\times&space;8$   $\inline&space;\fn_jvn&space;\Leftrightarrow$  X= $\inline&space;\fn_jvn&space;\frac{3\times&space;2\times&space;8}{4}$   $\inline&space;\fn_jvn&space;\Leftrightarrow$  x=12

11 6836
Q:

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?

 A) 75 B) 82 C) 100 D) 110

Explanation:

Originally let there be x men.

Less men, More days     (Indirect Proportion)

$\inline&space;\fn_jvn&space;\therefore$  (x-10) : x  :: 100 :110   $\inline&space;\fn_jvn&space;\Leftrightarrow$  $\inline&space;\fn_jvn&space;(x-10)\times&space;110=x\times&space;100$  $\inline&space;\fn_jvn&space;\Leftrightarrow$  10x= 1100    $\inline&space;\fn_jvn&space;\Leftrightarrow$  x= 110

13 6279
Q:

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

 A) 1 B) 3 C) 7 D) 14

Explanation:

Let the required number days be x.

Less spiders, More days (Indirect Proportion)

Less webs, Less days (Direct Proportion)

$\inline&space;{\color{Blue}&space;\left.\begin{matrix}&space;spiders&space;&1:7&space;\\&space;webs&space;&&space;7:1&space;\end{matrix}\right\}::7:x}$

$\inline&space;{\color{Blue}&space;\therefore&space;}$ 1 x 7 x x = 7 x 1 x 7

=> x= 7

16 6239
Q:

If 20 men can build a wall 56 meters long in 6 days , what length of  a similar wall can be  built by 35 men in 3 days?

 A) 46 B) 47 C) 48 D) 49

Explanation:

Let the required length be x meters

More men, More length built     (Direct proportion)

Less days, Less length built      (Direct Proportion)

$\inline&space;\fn_jvn&space;\left.\begin{matrix}&space;Men\:&space;\:&space;\:&space;20:35\\&space;Days\:&space;6:3&space;\end{matrix}\right\}::56:x$

$\inline&space;\fn_jvn&space;\therefore$  (20 x 6 x X)=(35 x 3 x 56) $\inline&space;\fn_jvn&space;\Leftrightarrow$  $\inline&space;\fn_jvn&space;x=\frac{35\times&space;3\times&space;56}{120}&space;=49$

Hence, the required length is 49 m.