Ratio, Proportion, Indices, LogarithmMCQMTP June 24 Series IIIQuestion 867 of 305
All Questions

The expenditures and savings of a person are in the ratio 4:1\displaystyle 4:1. If his savings are increased by 25%\displaystyle 25\% of his income, then what is the new ratio of his expenditure and savings ?

Options

A11:9\displaystyle 11:9
B8:5\displaystyle 8:5
C7:5\displaystyle 7:5
D7:4\displaystyle 7:4
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Correct Answer

✅ Option a — 11:9\displaystyle 11:9

All Options:

  • A11:9\displaystyle 11:9
  • B8:5\displaystyle 8:5
  • C7:5\displaystyle 7:5
  • D7:4\displaystyle 7:4

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Detailed Solution & Explanation

Let us represent the person's expenditure and savings as:
- Expenditure=4x\displaystyle \text{Expenditure} = 4x
- Savings=1x\displaystyle \text{Savings} = 1x
Since Income=Expenditure+Savings\displaystyle \text{Income} = \text{Expenditure} + \text{Savings}, the person's total income is:
Income=4x+1x=5x\text{Income} = 4x + 1x = 5x
Now, the savings are increased by 25%\displaystyle 25\% of his total income:
Increase in Savings=25% of 5x=0.25×5x=1.25x\text{Increase in Savings} = 25\% \text{ of } 5x = 0.25 \times 5x = 1.25x
The new savings amount is:
New Savings=Old Savings+Increase=1x+1.25x=2.25x\text{New Savings} = \text{Old Savings} + \text{Increase} = 1x + 1.25x = 2.25x
Assuming the total income remains constant (5x\displaystyle 5x), the new expenditure is:
New Expenditure=Income−New Savings=5x−2.25x=2.75x\text{New Expenditure} = \text{Income} - \text{New Savings} = 5x - 2.25x = 2.75x
Now, we calculate the new ratio of expenditure and savings:
New Ratio=New ExpenditureNew Savings=2.75x2.25x=2.752.25\text{New Ratio} = \frac{\text{New Expenditure}}{\text{New Savings}} = \frac{2.75x}{2.25x} = \frac{2.75}{2.25}
Multiply the numerator and denominator by 100\displaystyle 100 to clear the decimals:
New Ratio=275225\text{New Ratio} = \frac{275}{225}
Dividing both by their greatest common divisor, which is 25\displaystyle 25:
New Ratio=119=11:9\text{New Ratio} = \frac{11}{9} = 11:9
This matches **Option A**.
Hence, **Option A** is the correct answer.

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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