Question

A bag contains 50 p, 25 p and 10 p coins in the ratio 5 : 9 : 4, amounting to Rs.206. Find the number of coins of each type respectively.​

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

Given:-

A bag contains

• 50 paise coins
• 25 paise coins
• 10 paise coins

in the ratio 5 : 9 : 4.

Total amount in the bag = ₹ 206.

To find :-

• number of coins of each type respectively

Solution :-

Let x be the common multiple of the ratio 5 : 9 : 4

Hence,

50 paise = 5x

25 paise = 9x

10 paise = 4x

₹1 = 100 paise.

Convert the units into ₹,

50 paise = $\bf\large\frac{50}{100}$ = ₹ 0.5

25 paise = $\bf\large\frac{25}{100}$ = ₹ 0.25

10 paise = $\bf\large\frac{10}{100}$ = ₹ 0.1

5x (0.5) + 9x (0.25) + 4x (0.1) = 206

2.5x + 2.25x + 0.4x = 206

5.15x = 206

x = $\bf\large\frac{206}{5.15}$

Multiplying the numerator and denominator both by 100,

x = $\bf\large\frac{20600}{515}$

x = 40.

Value of common ratio, x = 40 coins.

Substitute this value in

• 5x
• 9x
• 4x

$\bf{\large{\underline{\boxed{\rm{\pink{50\: paise\:coins\: =\: 5x = 5 × 40 = 200}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\red{25\: paise\: coins\: = 9x = 9 × 40 = 360}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\blue{10\:paise\: coins\: = 4x = 4 × 40 = 160}}}}}}$