6
Q:

# Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in

 A) 6 days B) 12 days C) 4 days D) 3 days

Explanation:

Let x men can do the in 12 days and the required number of days be z

More men, Less days     [Indirect Proportion]

Less work, Less days     [Direct Proportion  ]

$\inline \fn_cm \left.\begin{matrix} Men & 2x:x\\ Work&1:\frac{1}{2} \end{matrix}\right\}::12:z$

$\inline \fn_cm \therefore (2x\times 1\times z)=(x\times \frac{1}{2}\times 12)$$\inline \fn_cm \Rightarrow 2xz=6x\Rightarrow z=3$

Q:

An industrial loom weaves 1.14 meters of cloth every second. Approximately, how much time will it take to weave 52 meters of cloth ?

 A) 29.32 sec B) 42.51 sec C) 39.25 sec D) 45.61 sec

Explanation:

Given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in,

1.14 ----- 1

52.0 ------?

$\inline \fn_jvn \Rightarrow$  $\inline&space;\dpi{100}&space;\frac{52}{1.14}$ = 45.61 sec

3 146
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.

21 2795
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.

26 5427
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

12 5919
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

$\inline&space;\fn_jvn&space;[(100\times&space;35)+(200\times&space;5)]$ 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.