Question

There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first, and twice the second is 36. The larger of the two is:
A) 3
B) 6
C) 9
D) 12
E) None of these

Answer 1

c) 9

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Answer 2

Given:

There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first, and twice the second is 36.

To find:

The larger of the two.

Solution:

Let the two numbers be x and y.

Now, according to the question, we have,

$2x + 3y = 39 \: \: (i)$

Also,

$3x + 2y = 36 \: \: (ii)$

Now,

On multiplying the (i) by 3 and (ii) by 2, we get

$6x + 9y = 117 \: \: (iii)$

and

$6x + 4y = 72 \: \: (iv)$

Now,

On subtracting (iv) from (iii), we have

$5y = 45$

on solving the above, we get

$y = 9$

Now, on putting the value of y in (i), we get

$3x + 2(9) = 36$

$3x + 18 = 36$

$3x = 18$

$x = 6$

Hence, the larger of the two numbers is C) 9.