Ratio, Proportion, Indices, LogarithmMCQMTP Sep 24 Series IIQuestion 872 of 302
All Questions

A bag contains $23$ number of coins in the form of $1rupee,\displaystyle rupee,2rupeeand\displaystyle rupee and5$ rupee coins. The total sum of the coins is $₹43$. The ratio between $1rupeeand\displaystyle rupee and2$ rupees coins is $3:2$. Then the number of 1\displaystyle 1 rupee coins.

Select Your Answer (Keyboard: A, B, C, D)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $12$

All Options:

  • A$12$
  • B8\displaystyle 8
  • C$10$
  • D$16$

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 $23$: x+y+z=23— (Equation 1)x + y + z = 23 \quad — (Equation 1)\displaystyle \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 — (Equation 2)\displaystyle \text{--- (Equation 2)} 3. The ratio between 1-rupee and 2-rupee coins is $3:2$. We can represent their numbers as: x=3kandy=2k— (Equation 3)x = 3k \quad and\displaystyle \text{and} \quad y = 2k \quad — (Equation 3)\displaystyle \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 — (Equation 4)\displaystyle \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 — (Equation 5)\displaystyle \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 ×\displaystyle \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.

More Questions from Ratio, Proportion, Indices, Logarithm

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

If the ratio of two numbers is $7:11.If\displaystyle . If7$ is added to each number then the new ratio will be $2:3$ then the numbers are.

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

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

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

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

Ready to Master Ratio, Proportion, Indices, Logarithm?

Practice all 302 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free