Question

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

Answer 1

Hint: A ratio is used to compare any two quantities of the same unit and is made by dividing one quantity by the other quantity of the same unit. We have been given the ratio of earnings of two persons A and B as 4:7.

Complete step-by-step answer:
let the earning of A be= $ 4x $
Let the earning of B be= $ 7x $
Now according to the given condition of increasing A’s earning by 50% and decreasing B’s by 25% when both have the earnings as a whole.
After the 50% increment, A’s earning be= 150% of $ 4x $ = $ \dfrac{{150}}{{100}} \times 4x = \dfrac{3}{2} \times 4x = 6x $
After the 25% decrement, B’s earning be= 75% of $ 7x $ = $ \dfrac{{75}}{{100}} \times 7x = \dfrac{3}{4} \times 7x = \dfrac{{21x}}{4} $
Further the new ratios of the earning of both A and B can be calculated by equating the above calculating earnings,
 $ 6x:\dfrac{{21x}}{4} $
To eliminate the denominator let us multiply by 4 on both the sides and cancel the terms common in both the numerator and denominator.
 $
\Rightarrow 4 \times 6x:21x \\
  24x:21x \;
  $
To determine the simplest ratio we have to divide by $ 3x $ from both the sides
 $ 8:7 $
We get the ratio as 8:7 which is the give ratio in the question. Though we were able to prove but we had to calculate the new earning of A which could have been possible if we would have been given total earning or amount of the earning of any one of A and B.
So, the correct answer is “Option D”.

Note: The answer is inadequate data because of this we could not determine the increment of A or its earning at any moment, as only ratios are given and the total earnings are unknown or any of the earnings is unknown.