Incomes of R and S are in the ratio 7:9 and their expenditures are in the ratio 4:5 . Their total expenditure is equal to income of R. What is the ratio of their savings?

Option d: 36:23. Solution: Let the incomes of R and S be 7x and 9x respectively. Let the expenditures of R and S be 4y and 5y respectively. Total expenditure = 4y + 5y = 9y . We are given that the total expenditure is equal to the income of R : 9y = 7x y = 7/9x Now we evaluate the savings ( S = Income - Expenditure ): - Savings of R = 7x - 4y = 7x - 4(7/9x) = 7x - 28/9x = 35/9x - Savings of S = 9x - 5y = 9x - 5(7/9x) = 9x - 35/9x = 46/9x The ratio of their savings is: Savings Ratio = 35/9x : 46/9x = 35 : 46

Ratio, Proportion, Indices, LogarithmMCQPYQ Dec 21Question 800 of 305

All Questions

Incomes of R and S are in the ratio $\displaystyle 7:9$ and their expenditures are in the ratio $\displaystyle 4:5$ . Their total expenditure is equal to income of R. What is the ratio of their savings?

Options

\displaystyle 23:36

\displaystyle 28:41

\displaystyle 23:33

\displaystyle 36:23

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Correct Answer

✅ Option d — $\displaystyle 36:23$

All Options:

A $\displaystyle 23:36$
B $\displaystyle 28:41$
C $\displaystyle 23:33$
D $\displaystyle 36:23$

Detailed Solution & Explanation

Let the incomes of

\displaystyle R

and

\displaystyle S

\displaystyle 7x

and

\displaystyle 9x

respectively.
Let the expenditures of

\displaystyle R

and

\displaystyle S

\displaystyle 4y

and

\displaystyle 5y

respectively.
Total expenditure

\displaystyle = 4y + 5y = 9y

.
We are given that the total expenditure is equal to the income of

\displaystyle R

9y = 7x \implies y = \frac{7}{9}x

Now we evaluate the savings (

\displaystyle S = \text{Income} - \text{Expenditure}

):
- Savings of

\displaystyle R = 7x - 4y = 7x - 4\left(\frac{7}{9}x\right) = 7x - \frac{28}{9}x = \frac{35}{9}x

- Savings of

\displaystyle S = 9x - 5y = 9x - 5\left(\frac{7}{9}x\right) = 9x - \frac{35}{9}x = \frac{46}{9}x

The ratio of their savings is:

\text{Savings Ratio} = \frac{35}{9}x : \frac{46}{9}x = 35 : 46

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.

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

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Incomes of R and S are in the ratio 7:9\displaystyle 7:97:9 and their expenditures are in the ratio 4:5\displaystyle 4:54:5. Their total expenditure is equal to income of R. What is the ratio of their savings?