Question

53. The ratio of the income of two persons is 9:7, and the ratio of their expenditure is 4:3. Each of them saves
* 200 yearly. Find their yearly income.
linear equation one variable question​

Answer 1

ANSWER:

Given:

• Ratio of incomes of 2 person = 9 : 7
• Ratio of expenditures of 2 person = 4 : 3
• Amount saved each year = Rs 200

To Find:

• Yearly income

Solution:

We are given that,

⟹ Ratio of incomes of 2 person = 9 : 7

So, the incomes will be 9x and 7x respectively.

⟹ Ratio of expenditures of 2 person = 4 : 3

So, the expenditures will be 4y and 3y respectively.

We know that,

⟹ Saving = Income - Expenditure

So, for Person 1,

⟹ 200 = 9x - 4y ------(1)

And, for Person 2,

⟹ 200 = 7x - 3y ------(2)

Multiplying (1) by 3 and (2) by 4,

⟹ 600 = 27x - 12y ------(3)

And,

⟹ 800 = 28x - 12y ------(4)

Subtracting (3) from (4),

⟹ 800 - 600 = 28x - 12y - 27x + 12y

⟹ 200 = x

So,

⟹ x = 200

Hence, yearly incomes are:

• Person 1 = 9x = 9 × 200 = 1800
• Person 2 = 7x = 7 × 200 = 1400

Therefore, the yearly incomes of them is Rs 1800 and Rs 1400 respectively.