The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3:2. However, each saves Rs. 6,000 per month. What is their total monthly income?a)Rs. 28,000b)Rs. 42,000c)Rs. 56,000d)Rs. 84,000Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Let's assume the monthly incomes of X and Y are 4x and 3x respectively, and their monthly expenses are 3y and 2y respectively. We are given that each person saves Rs. 6,000 per month.

1. Calculate the savings of X and Y:
The savings of X can be calculated as (4x - 3y) = 6000
The savings of Y can be calculated as (3x - 2y) = 6000

2. Solve the above equations simultaneously:
We can solve these two equations to find the values of x and y.
4x - 3y = 6000 ...(1)
3x - 2y = 6000 ...(2)

Multiply equation (1) by 2 and equation (2) by 3 to eliminate y:
8x - 6y = 12000 ...(3)
9x - 6y = 18000 ...(4)

Subtract equation (3) from equation (4):
(9x - 6y) - (8x - 6y) = 18000 - 12000
x = 6000

Substitute the value of x in equation (1) to find y:
4(6000) - 3y = 6000
24000 - 3y = 6000
-3y = 6000 - 24000
-3y = -18000
y = 6000

3. Calculate their total monthly income:
The total monthly income of X and Y can be calculated as:
Total Income = Income of X + Income of Y
= 4x + 3x
= 7x
= 7 * 6000
= Rs. 42,000

Therefore, their total monthly income is Rs. 42,000.

Hence, option B, Rs. 42,000, is the correct answer.

Answer

Given :

The ratio of the income of X and Y is 4 : 3.

The ratio of monthly expenses of X and Y is 3 : 2.

X and Y save 6000 rupees each month.

Concept used :

Savings = Income - expense

Calculations :

Let the ratio of monthly income of X and Y be 4a and 3a respectively.

Let the ratio of monthly expenses of X and Y be 3b and 2b respectively.

Savings of X = 4a - 3b

4a - 3b = 6000 ....(1)

Savings of Y = 3a - 2b

3a - 2b = 6000 ....(2)

Solving equation 1 and 2

We get a = 6000 and b = 6000

Total monthly income of X and Y = 4a + 3a = 7a

⇒ 7 × 6000

⇒ 42000 rupees

∴ Option 2 is the correct answer.

Answer

Since expenses and Savings are correlated
Therefore income of:
X=6000×4=24000
Y=6000×3=18000
x+y =24000+18000=42000(that is option 'B' is the right answer

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