Ratio, Proportion, Indices, LogarithmMCQMTP Sep 24 Series IIQuestion 872 of 305
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A bag contains 23\displaystyle 23 number of coins in the form of 1\displaystyle 1 rupee, 2\displaystyle 2 rupee and 5\displaystyle 5 rupee coins. The total sum of the coins is ₹43\displaystyle ₹43. The ratio between 1\displaystyle 1 rupee and 2\displaystyle 2 rupees coins is 3:2\displaystyle 3:2. Then the number of 1\displaystyle 1 rupee coins.

Options

A12\displaystyle 12
B8\displaystyle 8
C10\displaystyle 10
D16\displaystyle 16
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Correct Answer

✅ Option a — 12\displaystyle 12

All Options:

  • A12\displaystyle 12
  • B8\displaystyle 8
  • C10\displaystyle 10
  • D16\displaystyle 16

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Detailed Solution & Explanation

Let the number of 1-rupee, 2-rupee, and 5-rupee coins be x,y,\displaystyle x, y, and z\displaystyle z respectively.
We are given:
1. The total number of coins is 23\displaystyle 23:
x+y+z=23— (Equation 1)x + y + z = 23 \quad \text{--- (Equation 1)}
2. The total value of the coins is ₹43\displaystyle ₹43:
1x+2y+5z=43— (Equation 2)1x + 2y + 5z = 43 \quad \text{--- (Equation 2)}
3. The ratio between 1-rupee and 2-rupee coins is 3:2\displaystyle 3:2. We can represent their numbers as:
x=3kandy=2k— (Equation 3)x = 3k \quad \text{and} \quad y = 2k \quad \text{--- (Equation 3)}
where k\displaystyle k is a positive integer constant.
Let us substitute the expressions from Equation 3 into Equation 1 and Equation 2:
From Equation 1:
3k+2k+z=23  ⟹  5k+z=23  ⟹  z=23−5k— (Equation 4)3k + 2k + z = 23 \implies 5k + z = 23 \implies z = 23 - 5k \quad \text{--- (Equation 4)}
From Equation 2:
3k+2(2k)+5z=43  ⟹  7k+5z=43— (Equation 5)3k + 2(2k) + 5z = 43 \implies 7k + 5z = 43 \quad \text{--- (Equation 5)}
Substitute the expression for z\displaystyle z from Equation 4 into Equation 5:
7k+5(23−5k)=437k + 5(23 - 5k) = 43
Expand and solve for k\displaystyle k:
7k+115−25k=437k + 115 - 25k = 43
−18k=43−115-18k = 43 - 115
−18k=−72  ⟹  k=4-18k = -72 \implies k = 4
Now, we calculate the number of 1-rupee coins (x\displaystyle x):
x=3k=3×4=12x = 3k = 3 \times 4 = 12
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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