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 21,000
B. Rs 26,000
C. Rs 28,000
D. Data inadequate

Answer 1

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.
Hence, the correct answer is option (D.) Data inadequate.

Note: Basic approach to solve this type of questions is by applying algebra. Knowing the concept of rationalisation is the key. The data provided in the question is inadequate. For solving this type of question, earning at least one out of A and B should be known.