Question 41 of 49intermediate🔧 ApplyNumerical3 marks

Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total ₹88, how many coins does she have of each type?

Correct Answer

Let the number of five-rupee coins be x. Since Ruby has 3 times as many two-rupee coins, the number of two-rupee coins is 3x.

The total value of the five-rupee coins is 5x, and the total value of the two-rupee coins is 2×32 \times 3x = 6x.

The total amount Ruby has is ₹88. Therefore, we can form the equation: 5x + 6x = 88, which simplifies to 11x = 88.

Solving for x, we get x = 88 / 11 = 8. Thus, the number of five-rupee coins is 8. The number of two-rupee coins is 3×83 \times 8 = 24.

Exercise: Exercise Set 2.2 | Q: 5 | (Chapter: 6)
For More Understanding

Explanation

This problem involves forming a linear equation based on the given conditions. We define variables for the number of coins, express the total value as an equation, and solve for the variables to find the exact number of each coin type.

Solution Steps

  1. Step 1: Let the number of five-rupee coins be x. Then, the number of two-rupee coins is 3x.

  2. Step 2: The value of five-rupee coins is 5x, and the value of two-rupee coins is 2×32 \times 3x = 6x.

  3. Step 3: Form the equation for the total amount: 5x + 6x = 88, which gives 11x = 88.

  4. Step 4: Solve for x: x = 8. Therefore, five-rupee coins = 8 and two-rupee coins = 3×83 \times 8 = 24.

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