NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 8

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 8

Question:

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs 2000 per month, find their monthly incomes. Use elimination method

Given:

Ratio of incomes = 9 : 7
Ratio of expenditures = 4 : 3
Savings of each person = Rs 2000 per month

To Find:

Monthly incomes of the two persons

Formula:

Income - Expenditure = Savings

Solution:

Let the incomes be 9x and 7x, and expenditures be 4y and 3y.

9x - 4y = 2000 ...(1)
7x - 3y = 2000 ...(2)

Multiply (1) by 3 and (2) by 4 to eliminate y:

27x - 12y = 6000 ...(3)
28x - 12y = 8000 ...(4)

Subtract (3) from (4):
x = 2000

Substitute x = 2000 in (2):
7(2000) - 3y = 2000
14000 - 3y = 2000
3y = 12000
y = 4000

Incomes are 9x = 9(2000) = 18000 and 7x = 7(2000) = 14000

Result:

The monthly incomes of the two persons are Rs 18000 and Rs 14000.

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