Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by '25 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?

Options

A. `'80` lakh
B. `'50` lakh
C. `'40` lakh
D. `'60` lakh

Answer

To solve the problem step by step, let's denote the incomes of companies A and B as follows:

Let the income of company A = 5x (where x is a common multiplier)
Let the income of company B = 8x

According to the problem, if the income of company A had been increased by 25 lakh, the new income of company A would be:

New income of A = 5x + 25

The problem states that under this new condition, the ratio of their incomes becomes 5:4. Therefore, we can set up the following equation:

\[ \frac{5x + 25}{8x} = \frac{5}{4} \]

Now, we will cross-multiply to eliminate the fraction:

\[ 4(5x + 25) = 5(8x) \]

Expanding both sides gives us:

\[ 20x + 100 = 40x \]

Next, we will rearrange the equation to isolate x:

\[ 100 = 40x - 20x \]

This simplifies to:

\[ 100 = 20x \]

Now, we divide both sides by 20 to solve for x:

\[ x = 5 \]

Now that we have the value of x, we can find the income of company B:

\[ \text{Income of company B} = 8x = 8 \times 5 = 40 \text{ lakh} \]

Thus, the income of company B is **40 lakh**.

### Summary of Steps:
1. Let the incomes of A and B be represented as 5x and 8x respectively.
2. Set up the equation based on the new income of A and the given ratio.
3. Cross-multiply to eliminate the fraction.
4. Expand and rearrange the equation to isolate x.
5. Solve for x and substitute back to find the income of company B.