Select the correct answerA, B and C spend 80%, 85% and 75% of their incomes respectively. If their savings are in the ratio 8:9:20 and the difference between the incomes of A and C is Rs 18000, then the income of B is?OptionsRs 30000Rs 24000Rs 27000Rs 36000

Let's solve this step by step:

1. We know that income is the sum of expenditure and savings. So, if A, B, and C spend 80%, 85%, and 75% of their incomes respectively, that means they save 20%, 15%, and 25% of their incomes respectively.

2. The problem states that the savings of A, B, and C are in the ratio 8:9:20. This means that the savings of A is 8x, B is 9x, and C is 20x for some common multiplier x.

3. Since savings is a percentage of income, we can write the savings of A, B, and C in terms of their incomes. So, 20% of A's income is 8x, 15% of B's income is 9x, and 25% of C's income is 20x.

4. We can now write down the following equations based on the information above:

   0.20A = 8x 0.15B = 9x 0.25C = 20x

5. We also know that the difference between the incomes of A and C is Rs 18000. So, A - C = Rs 18000.

6. We can solve the above system of equations to find the values of A, B, and C.

7. From 0.20A = 8x, we get A = 40x. From 0.25C = 20x, we get C = 80x. Substituting these values in A - C = Rs 18000, we get 40x - 80x = Rs 18000, which simplifies to -40x = Rs 18000. Solving for x, we get x = -Rs 450.

8. But x cannot be negative, so we must have made a mistake. Let's correct it: A - C = Rs 18000 should be C - A = Rs 18000 (since C > A). So, 80x - 40x = Rs 18000, which simplifies to 40x = Rs 18000. Solving for x, we get x = Rs 450.

9. Now, we can find the income of B. From 0.15B = 9x, we get B = 9x / 0.15 = Rs 27000.

So, the income of B is Rs 27000.

Let's solve this step by step:

1. We know that income is the sum of expenditure and savings. So, if A, B, and C spend 80%, 85%, and 75% of their incomes respectively, that means they save 20%, 15%, and 25% of their incomes respectively.

2. The problem states that the savings of A, B, and C are in the ratio 8:9:20. This means that the savings of A is 8x, B is 9x, and C is 20x for some value of x.

3. Since savings is a percentage of income, we can write the savings of A, B, and C in terms of their incomes. So, 20% of A's income is 8x, 15% of B's income is 9x, and 25% of C's income is 20x.

4. We can now form equations from these relationships:

   20/100 * Income of A = 8x ----(1)

   15/100 * Income of B = 9x ----(2)

   25/100 * Income of C = 20x ----(3)

5. The problem also states that the difference between the incomes of A and C is Rs 18000. So, Income of A - Income of C = 18000 ----(4)

6. We can solve equations (1), (3), and (4) simultaneously to find the values of the incomes of A and C, and then substitute these values into equation (2) to find the income of B.

7. Solving equation (1) for Income of A, we get Income of A = 8x * 100/20 = 40x

8. Solving equation (3) for Income of C, we get Income of C = 20x * 100/25 = 80x

9. Substituting these values into equation (4), we get 40x - 80x = 18000, which simplifies to -40x = 18000, so x = -18000/40 = -450

10. But x cannot be negative, so there must be a mistake in our calculations. Let's go back and check.

11. In step 9, we should have subtracted 40x from 80x, not the other way around. So, the equation should be 80x - 40x = 18000, which simplifies to 40x = 18000, so x = 18000/40 = 450

12. Now we can substitute x = 450 into equation (2) to find the income of B. So, 15/100 * Income of B = 9 * 450, which simplifies to Income of B = 9 * 450 * 100/15 = Rs 27000

So, the income of B is Rs 27000. Therefore, the correct answer is Rs 27000.