# DBT JRF 2022 — Question 38

Exam: DBT JRF 2022 · Section: A · Topic: Aptitude › Fractions & Percentages · Difficulty: Medium

## Question

If the numerator of a fraction is increased by 15% and its denominator is decreased by 8%, the new fraction becomes 15/16. Find the original fraction.

## Options

- **A.** 4/3
- **B.** 15/4
- **C.** 3/4
- **D.** 4/15

## Answer

Option C

## Explanation

Fraction problem using algebra: Let the original fraction be $\frac{p}{q}$ . After the changes: numerator increases by 15%, denominator decreases by 8%: $\frac{1.15p}{0.92q} = \frac{15}{16}$ Solve for $\frac{p}{q}$ : $\frac{p}{q} = \frac{15}{16} \times \frac{0.92}{1.15} = \frac{15 \times 0.92}{16 \times 1.15} = \frac{13.8}{18.4} = \frac{138}{184} = \frac{3}{4}$ Verification: $\frac{3 \times 1.15}{4 \times 0.92} = \frac{3.45}{3.68} = \frac{345}{368} = \frac{15}{16}$ ✔ Answer: $\frac{3}{4}$ (Option 3).

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