2 children and 3 men can do a work in 12 days while 3 children and 2 men can do the same work in 10 days. How many days it will take to complete the same work if 1 child and 1 man work together?

A 27 days

B \(\frac{3}{{11}}days\)

C \(27\frac{3}{{11}}days\)

D 37 days

Correct Answer: Option C

Work done in 1 day by 2 children and 3 men,

2 C + 3 M = 1/12…………………(1)

Work done in 1 day by 3 children and 2 men,

3 C + 2 M = 1/10…………………..(2)

Solving equations (1) and (2) we get,

Work done in one day by 1 man,

M = 1/100

Work done in one day by 1 child,

C = 2/75

Total Work done in one day by 1 man and 1 child = 1/100 + 2/75 = 11/300

Hence, total time taken by them to complete the whole work =300/11 = \(27\frac{3}{{11}}days\)

Alternate Method (Short Trick):

Work done by 2 children and 3 man in 12 days = work done by 3 men and 2 children in 10 days,

Or, (2C + 3M) × 12 = (3C + 2M) × 10

Or, 24C + 36M = 30C + 20M,

Or, 16M = 6C,

Or, M = 3C/8

Now, Work done by 2 children and 3 men in 12 days = work done by 1 man and 1 child in X days (let),

∴ (2C + 3M) × 12 = (M + C) × X,

Putting the value of M in terms of C,

(2C + 9C/8) × 12 = (3C/8 + C) × X

Solving,

\(X = \frac{{300}}{{11}} = 27\frac{3}{{11}}\) days