57% of Ranita’s weekly income is equal to 76% of Bhaskar’s weekly income. If Ranita’s weekly income was reduced by ₹400, while Bhaskar’s weekly income did not change, the ratio of the weekly incomes of Ranita and Bhaskar, respectively, would have been 6 : 5. What is Bhaskar’s weekly income (in ₹)?

The correct answer is 3000.

Step-by-step explanation:

Step 1: Formulate the relationship between Ranita's and Bhaskar's weekly incomes.

Let Ranita's weekly income be $R$ and Bhaskar's weekly income be $B$.

According to the question, 57% of Ranita's weekly income is equal to 76% of Bhaskar's weekly income:

$57\%\text{of}R=76\%\text{of}B$

$\frac{57}{100}\times R=\frac{76}{100}\times B$

Simplifying by cancelling 100 from both denominators:

$57R=76B$

Dividing both sides by 19:

$3R=4B$

$R=\frac{4B}{3}$ — (Equation 1)

Step 2: Formulate the equation from the new ratio.

If Ranita's weekly income was reduced by ₹400, her new weekly income would be $R-400$.

The ratio of their weekly incomes (Ranita to Bhaskar) becomes 6 : 5:

$\frac{R-400}{B}=\frac{6}{5}$

Cross-multiplying the terms gives:

$5(R-400)=6B$

$5R-2000=6B$ — (Equation 2)

Step 3: Solve for Bhaskar's weekly income ($B$).

Substitute Equation 1 into Equation 2:

$5\left(\frac{4B}{3}\right)-2000=6B$

$\frac{20B}{3}-6B=2000$

Taking a common denominator:

$\frac{20B-18B}{3}=2000$

$\frac{2B}{3}=2000$

$2B=6000$

$B=3000$

Thus, Bhaskar’s weekly income is ₹3000.