Ratio, Proportion, Indices, LogarithmMCQMTP Jun 23 - Series IIQuestion 858 of 305
All Questions

The monthly income of A\displaystyle A & B\displaystyle B are in the ratio 4:5\displaystyle 4:5 are their monthly expenditures are in the ratio 5:7\displaystyle 5:7. If each saves ₹150\displaystyle ₹150 per month, find their monthly incomes.

Options

A(40,50)\displaystyle (40, 50)
B(50,40)\displaystyle (50, 40)
C(400,500)\displaystyle (400, 500)
DNone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — (400,500)\displaystyle (400, 500)

All Options:

  • A(40,50)\displaystyle (40, 50)
  • B(50,40)\displaystyle (50, 40)
  • C(400,500)\displaystyle (400, 500)
  • DNone of these

Ad

Detailed Solution & Explanation

Let the monthly incomes of A\displaystyle A and B\displaystyle B be 4x\displaystyle 4x and 5x\displaystyle 5x respectively.
Let the monthly expenditures of A\displaystyle A and B\displaystyle B be 5y\displaystyle 5y and 7y\displaystyle 7y respectively.
Since we know that Income−Expenditure=Savings\displaystyle \text{Income} - \text{Expenditure} = \text{Savings}, and each saves ₹150\displaystyle ₹150 per month, we can write the following system of linear equations:
4x−5y=150— (Equation 1)4x - 5y = 150 \quad \text{--- (Equation 1)}
5x−7y=150— (Equation 2)5x - 7y = 150 \quad \text{--- (Equation 2)}
Let us solve these equations for x\displaystyle x. Multiplying Equation 1 by 7\displaystyle 7 and Equation 2 by 5\displaystyle 5 to eliminate y\displaystyle y:
7(4x−5y)=7(150)  ⟹  28x−35y=1050— (Equation 3)7(4x - 5y) = 7(150) \implies 28x - 35y = 1050 \quad \text{--- (Equation 3)}
5(5x−7y)=5(150)  ⟹  25x−35y=750— (Equation 4)5(5x - 7y) = 5(150) \implies 25x - 35y = 750 \quad \text{--- (Equation 4)}
Subtract Equation 4 from Equation 3:
(28x−25x)+(−35y−(−35y))=1050−750(28x - 25x) + (-35y - (-35y)) = 1050 - 750
3x=300  ⟹  x=1003x = 300 \implies x = 100
Now we can determine the monthly incomes:
- Income of A=4x=4×100=₹400\displaystyle A = 4x = 4 \times 100 = ₹400
- Income of B=5x=5×100=₹500\displaystyle B = 5x = 5 \times 100 = ₹500
Thus, their monthly incomes are (400,500)\displaystyle (400, 500).
Hence, **Option C** 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.

More Questions from Ratio, Proportion, Indices, Logarithm

3x−2:5x+6\displaystyle 3x-2:5x+6 the duplicate ratio of 2:3\displaystyle 2:3 then find the value x\displaystyle x.

If the ratio of two numbers is 7:11\displaystyle 7:11. If 7\displaystyle 7 is added to each number then the new ratio will be 2:3\displaystyle 2:3 then the numbers are.

If x:y=z:7=4:11\displaystyle x:y=z:7=4:11 then x+y+zz\displaystyle \frac{x+y+z}{z} is

The ratio of two numbers are 3:4\displaystyle 3:4. The difference of their squares is 28\displaystyle 28 greater is:

The price of scooter and moped are in the ratio 7:9\displaystyle 7:9. The price of moped is ₹1,600\displaystyle ₹1,600 more than that of scooter. Then the price of moped is:

If A:B=3:7\displaystyle A:B=3:7, then 3a+2b:4a+5b=?\displaystyle 3a+2b:4a+5b=?

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