Question

(X+4) men can complete a work in 2X days while (X+12) women can complete same work in (X+8) days. If ratio of efficiency of men to women is 5 : 4 then find in how many days 12 men and 15 women together can complete the same work?​

Answer 1

i don't know please give me 5points

Answer 2

Answer:

16 days

Step-by-step explanation:

(X+4) men can complete a work in 2X days

So, 1 man can complete work in days = (X+4)(2X)

(X+12) women can complete same work in (X+8) days.

So,1 woman can compete work in days = (X+8)(X+12)

We are given that ratio of efficiency of men to women is 5 : 4

Since Efficiency is inversely proportional to time

So, ratio of time of men to women is 4:5

So, $\frac{4}{5}=\frac{\text{1 man time }}{\text{1 woman time }}$

$\frac{4}{5}=\frac{(X+4)(2X)}{ (X+8)(X+12)}$

$X=12$

1 man can complete work in days = (X+4)(2X) = (12+4)(2)(12) = 384

So, 1 man can do part of work in 1 day = $\frac{1}{384}$

So, 12 men can do part of work in 1 day = $\frac{12}{384}$

1 woman can compete work in days = (X+8)(X+12) =(12+8)(12+12)=480

So, 1 woman can do part of work in 1 day = $\frac{1}{480}$

So, 15 women can do part of work in 1 day = $\frac{15}{480}$

So, 12 men and 15 women together can do a part of work in 1 day = $\frac{12}{384}+\frac{15}{480} =\frac{1}{16}$

So,  12 men and 15 women together can do a 1/16 part of work in day = 1

12 men and 15 women together can do complete work in day = 16

Hence 12 men and 15 women together can complete the same work? in 16 days .