3
Q:

# A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

 A) 4 B) 9 C) 12 D) 49

Explanation:

Let the required number of revolutions made by larger wheel be x.

Then, More cogs, Less revolutions (Indirect Proportion)

${\color{Black}&space;\therefore&space;}$  14 : 6 :: 21 : ${\color{Black}&space;\Rightarrow&space;}$ 14 x x = 6 x 21

x=${\color{Black}&space;\frac{6\times&space;21}{14}&space;}$  ${\color{Black}&space;\Rightarrow&space;}$ x=9

Q:

If 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?

 A) 40 B) 50 C) 60 D) 70

Explanation:

Let the required no of hours be x. Then

Less men , More hours    (Indirct Proportion)

$\inline&space;\fn_jvn&space;\therefore$  15:36 ::25:x  $\inline&space;\fn_jvn&space;\Leftrightarrow$ (15 x X)=(36 x 25)  $\inline&space;\fn_jvn&space;\Leftrightarrow$ $\inline&space;\fn_jvn&space;x=\frac{36\times&space;25}{15}=60$

Hence, 15 men can do it in 60 hours.

19 2310
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.

24 4678
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

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

9 5071
Q:

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?

 A) 3 B) 5 C) 6 D) 9

Explanation:

$\inline&space;\fn_jvn&space;[(100\times&space;35)+(200\times&space;5)]$ men can finish the work in 1 day

$\inline&space;\fn_jvn&space;\therefore$  4500 men can finish the work in 1 day. 100 men can finish it in $\inline&space;\fn_jvn&space;\frac{4500}{100}$  = 45 days.

This is 5 days behind Schedule

4 2304
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

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