Question

If 378 coins consist of rupee, 50 paise and 25 paise coins, whose values are proportional to 13 :11 : 7, the number of 50 paise coins will be

Answer 1

Answer:

132 coins of 50 Paise

Step-by-step explanation:

Let say

1 Rs coin = X

50 Paise coins = Y

25 Paise coins = Z

X + Y + Z = 378

Value of 1 rs coin =  1 × X

Value of 50 Paise coins = (50/100) × Y = 0.5Y

Value of 25 Paise coins = (25/100) × Z = 0.25 Z

X : 0.5Y : 0.25Z = 13 : 11 : 17

Let a be common multiplier then

X = 13a

0.5Y = 11a => Y = 22a

0.25 Z = 7a => Z = 28a

X + Y + Z = 378

13a + 22a + 28a = 378

=> 63a = 378

=> a = 6

Number of 50 paise coins = Y = 22a = 22 × 6 = 132

132 coins

Answer 2

Let:-

Numbers of coins of 1 rupees, 50 paise and 25 paise are 13x, 11x and 7x respectively.

Then:-

Numbers of coins will be as

➤ 13x * 1 = 13x

➤ 11x * 2 = 22x

➤ 7x * 4 = 28x

Total = 63x

According to Question:-

➤ 63x = 378

➤ x = 378/63

➤ x = 6

Therefore:-

No. of 1 rupees coins, 13x = 6*1 = 6

No. of 50 paise coins, 22x = 22*6 = 132

No. of 25 paise coins, 28x = 28*6 = 168

Hence:-

Required answer is 132.