Question

# Ratio of the earnings of A and B is 4:7. If the earnings of A increases by 50% and those of B decreases by 25%, the new ratio of their earnings becomes 8:7. What are A's earnings?A. Rs 21,000B. Rs 26,000C. Rs 28,000D. Data inadequate

Hint: To solve this question we have used the concept of rationalisation. Taking x as rational we will try to find out the values of 4x and 7x and then apply a new ratio and solve the question accordingly.

Complete step-by-step solution -
Given the ratio of the earning of A and B is 4:7.
Let the rational between two earnings of A and B be x. Thus,
The earnings of A = 4x, and the earnings of B = 7x.
If the earnings of A increases by 50% and those of B decreases by 25%, the new ratio of their earnings becomes 8:7.
After earning of A increased by 50% then earnings of A will be:
$\Rightarrow 4x + \dfrac{{50}}{{100}}{\text{ of }}4x \\ \Rightarrow 4x + \dfrac{{4x}}{2} \\ \Rightarrow 4x + 2x \\ \Rightarrow 6x \\$
Similarly, after earnings of B decreased by 25% then earning of B will be:
$\Rightarrow 7x - \dfrac{{25}}{{100}}{\text{ of }}7x \\ \Rightarrow 7x - \dfrac{{7x}}{4} \\ \Rightarrow \dfrac{{\left( {28x - 7x} \right)}}{4}{\text{ }} \\ \Rightarrow \dfrac{{21x}}{4} \\ \Rightarrow 5.25x \\$
The ratio of their earnings if A's after increase and B's after decrease becomes 8:7,
$\Rightarrow 6x = 8 \\ \Rightarrow x = \dfrac{8}{6} \\ \Rightarrow x = 1.333 \\$
Similarly,
$\Rightarrow 5.25x = 7 \\ \Rightarrow x = \dfrac{7}{{5.25}} \\ \Rightarrow x = 1.333 \\$
Means the rational x is 1.333.
Thus, their earnings are:
A's earnings:
$\Rightarrow 4x{\text{ }} \\ \Rightarrow 4{\text{ }} \times {\text{ }}1.333{\text{ }} \\ \Rightarrow 5.332 \\$
B's earnings:
$\Rightarrow 7x \\ \Rightarrow 7{\text{ }} \times {\text{ }}1.333{\text{ }} \\ \Rightarrow 9.331 \\$
A's earning after 50% increase:
$\Rightarrow 6x{\text{ }} \\ \Rightarrow 6 \times 1.333 \\ \Rightarrow 7.998 = 8 \\$
B's earning after 25% decrease:
$\Rightarrow 5.25x{\text{ }} \\ \Rightarrow 5.25 \times 1.333 \\ \Rightarrow 6.998 = 7 \\$
The ratio after increase and decrease is 8:7 as given in question.
It means their earnings ratio derived 8:7 is matching the given ratio 8:7, but the data is inadequate to calculate exact individual earnings of A and B.