2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the

CuriousTab

Home Aptitude

Question
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
Options
A. 18 days
B. 21 days
C. 24 days
D. 30 days

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)

$\begin{array}{r} \begin{matrix} B o y s & 22 : 11 \end{matrix} \\ \begin{matrix} W o r k & 1 : 3 \end{matrix} \end{array}\} ? ? 14 : x$

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

=> x = 21

Hence, the required number of days = 21