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Pair of Linear Equations in Two Variables
NCERT Exemplar Ch 03
CBSE_NCERT_EXEMPLAR_CH03
Grade 10

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.

Step-by-Step Solution

Key Concept: Let incomes be $9x$ and $7x$, expenditures be $4y$ and $3y$. Equations: $9x - 4y = 2000$ and $7x - 3y = 2000$.
Stepwise Solution:

System: $9x - 4y = 2000$ -- (eq 1) and $7x - 3y = 2000$ -- (eq 2). [1.0 Mark]

Multiply eq 1 by 3: $27x - 12y = 6000$.
Multiply eq 2 by 4: $28x - 12y = 8000$.
Subtract: $(28x - 12y) - (27x - 12y) = 8000 - 6000 \Rightarrow x = 2000$. [1.0 Mark]

Monthly income of 1st person $= 9 \times 2000 = \text{Rs } 18000$.
Monthly income of 2nd person $= 7 \times 2000 = \text{Rs } 14000$. [1.0 Mark]

Marking Scheme:

• Forming system of linear equations: 1.0 Mark
• Solving by elimination for $x = 2000$: 1.0 Mark
• Calculating monthly incomes (Rs 18,000 and Rs 14,000): 1.0 Mark

Correct Answer:
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