Question

The income of A and B are in the ratio of 3:4 and their expenditures are in the ratio of 5:7. If each saves Rs 1000, find their incomes

Answer 1

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Let income of A and B be 3x and 2x respectively. Also, their expenditure is 5y and 3y.

Now, according to question,

3x - 5y = 1000 ------- (i) × 3

2x - 3y = 1000 ---------- (ii) × 5

9x - 15y - 10x + 15y = 3000 - 5000

Or, -x = -2000

Or, x = 2000

Then, income of A = 3x = 3 × 2000 = Rs. 6000

Answer 2

ATQ:

The income of A & B is in the ratio 3:4.

A's Income ➞ 3x.

B's Income ➞ 4x.

The expenditure of A & B is in the ratio 5:7.

A's Expenditure ➞ 5y

B's Expenditure ➞ 7y

Both of their savings is Rs. 1000.

We know that:

$\boxed{\sf Savings = Income - Expenditure}$

∴ A's savings will be:

➞ A's Income - A's Expenditure = A's Savings

➞ 3x - 5y = 1000 ⇔ Eq(1)

∴ B's savings will be:

➞ B's Income - B's Expenditure = B's Savings

➞ 4x - 7y = 1000 ⇔ Eq(2)

Eq(1) × 4 ⇒ 12x - 20y = 4000 ⇔ Eq(3)

Eq(2) × 3 ⇒ 12x - 21y = 3000 ⇔ Eq(4)

Subtract Eq(3) from Eq(4):

➞ 12x - 21y - (12x - 20y) = 3000 - 4000

➞ 12x - 21y - 12x + 20y = -1000

➞ -21y + 20y = -1000

➞ -y = -1000

➞ y = 1000

Substitute the value of y in Eq(3):

➞ 12x - 20y = 4000

➞ 12x - 20(1000) = 4000

➞ 12x - 20000 = 4000

➞ 12x = 4000 + 20000

➞ 12x = 24000

➞ x = 24000/12

➞ x = 2000

Therefore:

A's Income ➞ 3x ➞ 3(2000) ➞ 6000Rs.

B's Income ➞ 4x ➞ 4(2000) ➞ 8000Rs.