Question

The ratio between two numbers is 19: 24. If each number is reduced by 36, the ratio becomes 3: 4. Find the sum of the numbers.

• A. 387
• B. 305
• C. 238
• D. 295

Answer 1

Answer:

A. 387

Let the two numbers be 19x and 24x.

After reducing each by 36, the ratio becomes 3 : 4:

$\frac{19x - 36}{24x - 36} = \frac{3}{4}$
Cross-multiply:

$4(19x - 36) = 3(24x - 36)$
$76x - 144 = 72x - 108$
$4x = 36$
$\Rightarrow x = 9$

Numbers:

First number = $(19 \times 9 = 171)$

Second number = $(24 \times 9 = 216)$

Sum:
$171 + 216 = \boxed{387}$

Sum of the numbers = 387