Question

A box contains ₹2, ₹1 and 50p coins in the ratio 3:4:5. If the total value is ₹250, find the number of 50p coins.

• A. 50
• B. 100
• C. 125
• D. 150

Answer 1

Answer:

B. 100

To find the number of 50 paise coins, let's break down the problem step-by-step using the given ratio of their counts.

Given Data:

• Ratio of the number of coins (Rs 2 : Rs 1 : 50 paise) = $3 : 4 : 5$

• Total value of all coins = ₹250

Step-by-Step Calculation:

1. Assign variables to the number of coins: Let the number of:

   
   

   • Rs 2 coins = $3x$

   • Rs 1 coins = $4x$

   • 50 paise coins = $5x$

2. Calculate the total value in terms of rupees ($x$):

   
   

   • Value of Rs 2 coins = $3x \times 2 = 6x$

   • Value of Rs 1 coins = $4x \times 1 = 4x$

   • Value of 50 paise coins = $5x \times 0.50 = 2.5x$  (since 50 paise = ₹0.50)

3. Set up the equation using the total value:

   
   

   $\text{Total Value} = 6x + 4x + 2.5x = 12.5x$

   We are given that the total value is ₹250:

   
   

   $12.5x = 250$

4. Solve for $x$:

   
   

   $x = \frac{250}{12.5}$

   $x = 20$

5. Find the number of 50 paise coins:

   
   

   $\text{Number of 50 paise coins} = 5x = 5 \times 20 = 100$

Answer:

There are 100 50-paise coins in the box.