2
Q:

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?

A) 10 B) 13
C) 14 D) 15

Answer:   B) 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)

\inline {\color{Blue} \left.\begin{matrix} persons &30:39 \\ working\; hours/day & 6:5 \end{matrix}\right\}::12:x}

\inline {\color{Blue} \therefore } 30 x 6 x x = 39 x 5 x 12

=> x= \inline {\color{Blue}\frac{39\times 5\times 12}{30\times 6}}

=> x= 13

 

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
 
Answer & Explanation Answer: C) 60

Explanation:

Let the required no of hours be x. Then

Less men , More hours    (Indirct Proportion)

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

Hence, 15 men can do it in 60 hours.

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19 2292
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
 
Answer & Explanation Answer: 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 \fn_jvn \left.\begin{matrix} Men\: \: \: 20:35\\ Days\: 6:3 \end{matrix}\right\}::56:x

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

Hence, the required length is 49 m.

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24 4632
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 \fn_jvn (2\times 14) men +(7\times 14)boys=(3\times 11)men+(8\times 11)boys

\inline \fn_jvn \Leftrightarrow  5 men= 10 boys  \inline \fn_jvn \Leftrightarrow  1man= 2 boys

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

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

Hence, the required number of days = 21

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9 4985
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
 
Answer & Explanation Answer: B) 5

Explanation:

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

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

This is 5 days behind Schedule

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4 2289
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
 
Answer & Explanation Answer: D) 110

Explanation:

Originally let there be x men.

Less men, More days     (Indirect Proportion)

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

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11 4762