Question

A bag contains Rs 750 in the form of rupee, 50 P and 25 P coins in the ratio 5 : 8 : 4. Find the number of coins of each type.

Answer 1

Let the numbers one rupee, fifty paise and twenty-five paise coins be 5x, 8x and 4x, respectively.

Total value of these coins = ($5x\times \frac{100}{100}+8x\times \frac{50}{100}+4x\times \frac{25}{100}$)

$$\begin{gathered} \Rightarrow 5x+\frac{8x}{2}+\frac{4x}{4} \\ =\frac{20x+16x+4x}{4}=\frac{40x}{4}=10x \end{gathered}$$

However, the total value is Rs 750.
∴ 750 = 10x
⇒ x = 75

Hence, number of one rupee coins = 5 $\times$ 75 = 375
Number of fifty paise coins = 8 $\times$ 75 = 600
Number of twenty-five paise coins = 4 $\times$ 75 = 300