Question

A father gives Rs. 500 to his children every month. If the boy gets Rs. 100 then, the girl gets Rs. 200 and if the boy gets Rs. 100 the girl gets Rs. 150. How many children does he have?

(a) 0

(b) 3

(c) 2

(d) 1

I had been asked this question by my college professor while I was bunking the class.

The doubt is from Solution of Two Linear Equations in Two Variables in Different Methods in section Pair of Linear Equations in Two Variables of Mathematics – Class 10

Answer 1

The correct option is (b) 3

Easy explanation: Let the number of boys be x and number of girls be y

Now, if the boys get 100, the girls get 200

100x+200y=500

x+2y=5

x=5-2y

If the boys get 200, the girls get 150

200x+150y=500

4x+3y=10     (1)

Substituting x=5-2y in equation 1 we get,

4(5-2y)+3y=10

20-8y+3y=10

-5y=-10

y=2

x=5-2y=5-2(2)=1

The father has three children.