Question

5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between efficincies of a man an boy

Answer 1

Answer:

ratio of efficiency is 6 : 5

Step-by-step explanation:

Let the amount of work done by 1 man per day be $m$

Let the amount of work done by 1 boy per day be $n$

Given that 5 men and 12 boys can do a piece of work in 4 days

Thus, work done by 5 men and 12 boys in 1 day $= \frac{1}{4}$

We get,

$5m + 12n = \frac{1}{4}\\\\20m + 48n = 1$

Similarly,

7 men and 6 boys can do a piece of work in 5 days

Thus, work done by 7 men and 6 boys in 1 day $= \frac{1}{5}$

We get,

$7m + 6n = \frac{1}{5}\\\\35m + 30n = 1$

Solving the two equations

 20m + 48n = 1   ---- × 7

 35m + 30n = 1  ---- × 4

-----------------------------------

 140m + 336n = 7

 140m + 120n = 4

(-)        (-)        (-)

---------------------------

           216n = 3

             n = $\frac{3}{216}$

             n = $\frac{1}{72}$

Putting the value of $n$, we get

$20m + 48 \times \frac{1}{72} = 1\\\\ 20m + \frac{48}{72} = 1\\\\20m + \frac{2}{3}= 1\\\\20m = 1 - \frac{2}{3}\\\\20m = \frac{1}{3}\\\\m = \frac{1}{(\,3 \times 20)\,}\\\\m = \frac{1}{60}$

Man's 1 day work $= \frac{1}{60}$

Thus, Efficiency of man $= \frac{100}{60} = \frac{5}{3}$

Boy's 1 day work $= \frac{1}{72}$

Thus, Efficiency of boy $= \frac{100}{72} = \frac{25}{18}$

Ration of efficiency of a man and a boy is calculated as

$\frac{\frac{5}{3}}{\frac{25}{18}}\\\\ \frac{(\,5 \times 18)\,}{(\,25 \times 3)\,}\\\\ \frac{6}{5}$

Thus, ratio of efficiency is 6 : 5