Question Details

Suman’s earnings in a month are five-sevenths of Meera’s. In the next month, Meera’s earnings become five-eighths of Suman’s previous month earnings. By what percent are Meera’s current earnings less than Suman’s current earnings?

Options

20%

37.5%

35.5%

25%

Show Answer

Correct Answer :

Option B

37.5%

Solution :

The correct option is 37.5%.

Let us break down the problem step-by-step to understand why this is the correct answer.

Step 1: Define the initial earnings of Suman and Meera.
Let Suman's initial earnings (in the first month) be $S_{1}$ and Meera's initial earnings be $M_{1}$ .
According to the problem statement, Suman's earnings in a month are five-sevenths of Meera's. We can write this relation as:

$S_{1} = \frac{5}{7} M_{1}$

To make the calculations simple and avoid working with fractions, let us assume Meera's initial earnings are a convenient multiple of 7, say:

$M_{1} = 56$

Using this value, we can find Suman's initial earnings:

$S_{1} = \frac{5}{7} \times 56 = 5 \times 8 = 40$

Step 2: Determine Meera's current (next month's) earnings.
In the next month, Meera's earnings ( $M_{2}$ ) become five-eighths of Suman's previous month's earnings ( $S_{1}$ ). Mathematically, this is expressed as:

$M_{2} = \frac{5}{8}$

Substituting the value of $S_{1} = 40$ into the equation, we get:

$M_{2} = \frac{5}{8}$

Thus, Meera's current earnings are 25.

Step 3: Identify Suman's current earnings.
Since there is no mention of any change in Suman's earnings, Suman's current earnings remain the same as the previous month:

$S_{2} = S_{1} = 40$

Step 4: Calculate by what percent Meera's current earnings are less than Suman's current earnings.
We need to find the percentage difference relative to Suman's current earnings. The formula is:

$Percentage Less = \frac{S_{2} - M_{2}}{S_{2}} \times 100$

Substitute the values $S_{2} = 40$ and $M_{2} = 25$ into the formula:

$Percentage Less = \frac{40 - 25}{40} \times 100$

$Percentage Less = \frac{15}{40} \times 100$

Simplify the fraction:

$Percentage Less = \frac{3}{8} \times 100$

$Percentage Less = 0.375 \times 100 = 37.5 %$

Therefore, Meera's current earnings are 37.5% less than Suman's current earnings.