# Linear equation problem for aptitude exam

This is a question that has been asked by my teacher who is helping me prepare for the Common Admission Test conducted in India for admission into postgraduate management programmes of Indian universities.

Question: If the boys of a class wear one shirt each, 4 shirts remain extra. If each boy wears 2 shirts each, two boys are left shirtless. How many boys are there in the class?

I know that the answer is 8 boys. I arrived at the answer by trial and error. But I want a definite approach which can help arrive at the right answer quickly.

The number of boys : B

The number of Shirts : S

$$B + 4 = S$$ $$2(B-2) = S$$

Solve the system of equation $$B - 8 = 0$$

Therefore, B = 8.

Hint. If there are $$B$$ boys in the class the first condition says there are $$B+4$$ shirts.

Can you write the equation for the number of shirts that comes from the second condition? Then set those two expressions equal and solve for $$B$$.

• that's where I am struggling man!! – Shahbaaz Sheikh Apr 11 at 1:55
• See the answer from @SPhilKim . – Ethan Bolker Apr 11 at 1:59
• I got it after a few minutes! Thanks for the help! – Shahbaaz Sheikh Apr 11 at 2:16