$57\%$ of Ranita’s weekly income is equal to $76\%$ of Bhaskar’s weekly income. If Ranita’s weekly income was reduced by $\text{₹}400$, 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 $\text{₹}$)?

Let Ranita's weekly income be $R$ and Bhaskar's weekly income be $B$.
From the first condition given in the problem:

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

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

$$57R=76B$$

Finding the ratio of their weekly incomes:

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

Dividing both numerator and denominator by $19$:

$$\frac{R}{B}=\frac{4}{3}$$

So, let Ranita's weekly income be $4x$ and Bhaskar's weekly income be $3x$.

According to the second condition, if Ranita's income decreases by $\text{₹}400$ while Bhaskar's remains unchanged, their new income ratio is $6:5$:

$$\frac{4x-400}{3x}=\frac{6}{5}$$

Now, cross-multiply to solve for $x$:

$$5(4x-400)=6(3x)$$

$$20x-2000=18x$$

$$20x-18x=2000$$

$$2x=2000$$

$$x=1000$$

Bhaskar's weekly income is represented by $3x$:

$$\text{Bhaskar’s weekly income}=3\times 1000=3000$$

Thus, Bhaskar's weekly income is $\text{₹}3000$.