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 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

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, LogarithmPYQ 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

For any discrepancies in this question, email contact@cadada.in

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.

Ready to Master Ratio, Proportion, Indices, Logarithm?

Practice all 305 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

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: