Question

some one rupee ,50 paise and 25 paise coins make up rupees 20 and their numbers are in the ratio proportion of 4:1:2 find the numbers of each type of coins​

Answer 1

Solution :

• 1 rupee = 100 paise
• 20 rupees = 2000 paise

By the given condition, numbers of one rupee, 50 paise and 25 paise coins are in the ratio 4 : 1 : 2.

If we take x as a common multiple, the number of 1 rupee coin is 4x, the number of 50 paise coin is x and for 25 paise, it is 2x.

Given,

(100 * 4x) + (50 * x) + (25 * 2x) = 2000

⇒ 400x + 50x + 50x = 2000

⇒ 500x = 2000

⇒ x = 4

Hence, the number of

• one rupee coins = 4 * 4 = 16
• 50 paise coins = 4
• 25 paise coins = 2 * 4 = 8

( Answer )

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

There are 16 One rupee coins, 50 paise coins are 4 in Number and 8 coins of 25 paise.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

There are -

• One Rupee coins
• 50 paise coins
• 25 paise coins

Ratio = 4 : 1 : 2

Total money = Rs. 20

To Find :

The number of each type of coins.

Solution :

$\textbf{\small{\underline{Consider the -}}}$

• One Rupee coins as 4x
• 50 Paise coins as 1x
• 25 Paise coins as 2x

Convert Rs.20 into paise

$\longrightarrow$ 20 × 100...... [ 1 Rupee = 100 paise ]

$\longrightarrow$ 2000

★ $\boxed{\sf{100(4x) + 50(x) + 25(2x) = 2000}}$

$\tt{\longrightarrow} \: 100(4x) + 50(x) + 25(2x) = 2000$

$\tt{\longrightarrow} \: 400x + 50x + 50x = 2000$

$\tt{\longrightarrow} \: 400x + 100x = 2000$

$\tt{\longrightarrow} \: 500x = 2000$

$\tt{\longrightarrow} \: x = \dfrac{2000}{500}$

$\tt{\longrightarrow} \: x = 4$

$\rule{300}{1.5}$

★ Value of 4x

$\tt{\longrightarrow} \: 4 \times 4$

$\tt{\longrightarrow} \: 16$

One Rupee coins = 16 coins

$\rule{300}{1.5}$

★ Value of 2x

$\tt{\longrightarrow} \: 4 \times 2$

$\tt{\longrightarrow} \: 8$

25 paise Coins = 8 coins

$\therefore$ There are 16 One rupee coins, 50 paise coins are 4 in Number and 8 coins of 25 paise.