Discussion

Two numbers are in the ratio 3:5. If 12 is added to both the numbers, then the ratio becomes 5:7. The sum of the given two numbers is

Answer: C

The sum of the two numbers is 48.

Let the numbers be \(3x\) and \(5x\). Adding 12 to each gives the new ratio 5:7.

\[ \begin{aligned} \frac{3x + 12}{5x + 12} &= \frac{5}{7} \\ 21x + 84 &= 25x + 60 \\ 4x &= 24, \quad x = 6 \end{aligned} \]

The numbers are 18 and 30, and their sum is \(8x = 48\). Check: \(18 + 12 = 30\) and \(30 + 12 = 42\), and \(30 : 42 = 5 : 7\).

The other sums (32, 40, 56) are multiples of 8 too, but only \(x = 6\) satisfies the changed ratio.

No comment is present. Be the first to comment.

Loading…