During our campaign against child labour we have found that in three glass making factories

Ques - During our campaign against child labour we have found that in three glass making factories A, B and C there were total 33 children aged below 18 were involved. The ratio of male to female in A, B and C was 4 : 3, 3 : 2 and 5 : 4 respectively. If the no. of female children working in the factories B and C be equal, then find the no. of female children working in factory A?​

(a) 5

(b) 2

(c) 8

(d) 6

Solution - 

We have,

Total of 33 children aged below 18 were involved.

The ratio of male to female in A, B and C was 4 : 3, 3 : 2 and 5 : 4 respectively.

The number of male and female in factories A, B & C are:

        Male        Female

A:      4x                3x

B:      3y               2y

C:      5z               4z

If the no. of female children working in the factories B and C be equal.

So,

No. of female children in B = No. of female children in C

⇒ 2y = 4z

⇒ y = 2z

Now,

Total no. of children in factories A, B & C = 33

⇒ (4x + 3x)  + (3y + 2y) + (5z + 4z) = 33

⇒ (7x) + (5y) + (9z) = 33

⇒ (7x) + [5(2z)] + (9z) = 33   (given - y = 2z )

⇒ 7x + 10z + 9z = 33

⇒ 7x + 19z = 33

Thus,

The only value possible for z is 1

⇒ 7x + (19×1) = 33

⇒ 7x + 19 = 33

⇒ 7x = 33 - 19

⇒ 7x = 14

⇒ x = 2

Therefore,

No. of female children working in factory A = 3x

= 3 × 2

= 6

Thus, 

The no. of female children working in factory A is 6.

Hence,

The correct answer is option (d) 6.

Thank You