Question

Find two numbers such that the larger number added to three times the smaller number gives 7 and twice the larger number added to the smaller number gives 9.

• A. 1, 4
• B. 2, 5
• C. 4, 7
• D. None of these

Answer 1

The correct option is A

1, 4

Let the larger number be x and the smaller number be y.

x + 3y = 7 …(i)

2x + y = 9 …(ii)

On multiplying (i) by 2 and (ii) by 1, we get

2x+6y=14

2x+y=9

Solving the above two equations, we get

$5y=5$

Or $y=\frac{5}{5}=1$

On substituting value of y in (i), we get

x + 3$\times$1 = 7

or x + 3 = 7

or x = 7 – 3 = 4

$\therefore$ Larger number is 4 and smaller number is 1.