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Mathematics · Pair of Linear Equations in Two Variables · NCERT Examples

Example 8

A complete, independently verified solution for NCERT Example 8.

Mathematics · Chapter 3 · NCERT Examples

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NCERT Example

Example 8

elimination method · word problem

Income ratio is 9 : 7, expenditure ratio is 4 : 3, and each person saves ₹2000 monthly. Find their incomes.

Solution

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

9x−4y=2000,7x−3y=20009x-4y=2000,\qquad7x-3y=2000
27x−12y=6000,28x−12y=800027x-12y=6000,\qquad28x-12y=8000
x=2000,y=4000x=2000,\qquad y=4000
9x=18000,7x=140009x=18000,\qquad7x=14000

The expenditures are ₹16000 and ₹12000, ratio 4 : 3; each saving is ₹2000.

Final answer

The monthly incomes are ₹18,000 and ₹14,000.