The ratio of income of A and B is 5:4 and their expenditure is 3:2 . If at the end of the year each saves ₹1,600 , then the income of A is:

Option c: ₹4,000. Solution: Let the incomes of A and B be 5x and 4x , and their expenditures be 3y and 2y respectively. Each saves ₹1,600 at the end of the year: 5x - 3y = 1600 (1) 4x - 2y = 1600 (2) From equation (2), dividing both sides by 2 gives: 2x - y = 800 y = 2x - 800 Substitute this expression for y into equation (1): 5x - 3(2x - 800) = 1600 5x - 6x + 2400 = 1600 -x = 1600 - 2400 -x = -800 x = 800 The income of A is: Income of A = 5x = 5(800) = ₹4,000

The ratio of income of A and B is $5:4$ and their expenditure is $3:2$. If at the end of the year each saves $₹1,600$, then the income of A is:

The correct answer is Option c: $₹4,000$. Let the incomes of $A$ and $B$ be $5x$ and $4x$, and their expenditures be $3y$ and $2y$ respectively. Each saves $₹1,600$ at the end of the year: $$5x - 3y = 1600 \quad (1)$$ $$4x - 2y = 1600 \quad (2)$$ From equation (2), dividing both sides by $2$ gives: $$2x - y = 800 \implies y = 2x - 800$$ Substitute this expression for $y$ into equation (1): $$5x - 3(2x - 800) = 1600$$ $$5x - 6x + 2400 = 1600$$ $$-x = 1600 - 2400$$ $$-x = -800 \implies x = 800$$ The income of $A$ is: $$\text{Income of A} = 5x = 5(800) = ₹4,000$$

Ratio, Proportion, Indices, LogarithmMCQPYQ Sep 24Question 810 of 305

All Questions

The ratio of income of A and B is $\displaystyle 5:4$ and their expenditure is $\displaystyle 3:2$ . If at the end of the year each saves $\displaystyle ₹1,600$ , then the income of A is:

Options

\displaystyle ₹3,600

\displaystyle ₹3,400

\displaystyle ₹4,000

\displaystyle ₹4,200

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Correct Answer

✅ Option c — $\displaystyle ₹4,000$

All Options:

A $\displaystyle ₹3,600$
B $\displaystyle ₹3,400$
C $\displaystyle ₹4,000$
D $\displaystyle ₹4,200$

Detailed Solution & Explanation

Let the incomes of

\displaystyle A

and

\displaystyle B

\displaystyle 5x

and

\displaystyle 4x

, and their expenditures be

\displaystyle 3y

and

\displaystyle 2y

respectively.
Each saves

\displaystyle ₹1,600

at the end of the year:

5x - 3y = 1600 \quad (1)

4x - 2y = 1600 \quad (2)

From equation (2), dividing both sides by

\displaystyle 2

gives:

2x - y = 800 \implies y = 2x - 800

Substitute this expression for

\displaystyle y

into equation (1):

5x - 3(2x - 800) = 1600

5x - 6x + 2400 = 1600

-x = 1600 - 2400

-x = -800 \implies x = 800

The income of

\displaystyle A

is:

\text{Income of A} = 5x = 5(800) = ₹4,000

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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The ratio of income of A and B is 5:4\displaystyle 5:45:4 and their expenditure is 3:2\displaystyle 3:23:2. If at the end of the year each saves ₹1,600\displaystyle ₹1,600₹1,600, then the income of A is: