Question

5 men and 6 women can do a piece of work in 6 days while 3 men and 5 women can do the same work in 9 days. In how many days can 3 men and 2 women do the same work?

• A. $$11\frac{5}{11}$ days$
• B. $$13\frac{3}{11}$ days$
• C. $$10\frac{9}{11}$ days$
• D. $$12\frac{1}{11}$ days$

Answer 1

Answer:

$$11\frac{5}{11}$ days$

$5M+6W=6$ days

$3M+5W=9$ days

total work is same

$(5M+6W)6=(3M+5W)9$

$(5M+6W)2=(3M+5W)3$

$10M+12W=9M+15W$

$M=3W$

$\frac{M}{W}=\frac31$

work$=(5\times 3+6\times 1)6=126$

the days is

$3M+2W=3\times 3+2\times 1=9+2=11$

$\frac{126}{11}=11\frac{5}{11}$ days