Question

The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and the second to the third is 5:8, what is the second number?

• A. 30
• B. 35
• C. 40
• D. 45

Hint:

Express all terms in a single variable using ratios and solve for the sum.

Answer 1

The Correct Option is A

- Step 1: Let the numbers be $a, b, c$. Given $a:b = 2:3$, $b:c = 5:8$.
- Step 2: Express in terms of $b$: $a = \frac{2}{3}b$, $c = \frac{8}{5}b$.
- Step 3: Sum = $a + b + c = 98 \implies \frac{2}{3}b + b + \frac{8}{5}b = 98$.
- Step 4: LCM of 3, 5 is 15. So, $\frac{10b + 15b + 24b}{15} = 98 \implies 49b = 98 \times 15 \implies b = 30$.
- Step 5: Verify: $a = \frac{2}{3} \times 30 = 20$, $c = \frac{8}{5} \times 30 = 48$. Sum = $20 + 30 + 48 = 98$.
- Step 6: Option (1) is 30, correct.