Question

a bag contains one rupee ,50 and 25 p coins in the ratio 5:6:8 amounting to rupees 120 find the number of coins of each type​

Answer 1

Below I have given step by step solution......!!!

Step-by-step explanation:

The ratio of Rs.1, 50 paise and 25 paise coins is 5:6:8∴

Number of Rs.1 coins = 5x.

⇒ Number of 50paise coins = 6x

⇒ Number of 25paise coins = 8x.∴

Value of 5x Rs.1 coins = Rs.1×5x=Rs.5x

⇒ Value of 6x 50paise coins = 6x×50paise=Rs. 6x×50/100 =Rs.3x

⇒ Value of 8x 25paise coins = 8x×25paise=Rs. 8×25/100 =Rs.2x

⇒ Total amount = Rs.120∴ 5x+3x+2x=120∴

10x=120∴

x= 120/10 =12∴

Number of Rs.1 coins = 5×12=60∴ Number of 50paise coins = 6×12=72∴ Number of 25paise coins = 8×12=96

⇒ Total number of coins = 60+72+96=228

Hope you get it.....!!

Answer 2

${\underline{\underline{\bf{Given:}}}}$

• A bag contains one rupee coins, 50 paise coins and 25 paise coins.
• They're in the ratio of 5 : 6 : 8
• The sum of their value (amount) is 120/-

${\underline{\underline{\bf{To\:find:}}}}$

• The number of coins in each type.

${\underline{\underline{\bf{Solution:}}}}$

$\sf{Let,}$

$\rightarrow$The number of 1 rupee coins be $\sf{5x}$.

$\rightarrow$The number of 50 paise coins be $\sf{6x}$.

$\rightarrow$The number of 25 paise coins be $\sf{8x}$.

$\sf{As\:we\:know,}$

$\underline{\boxed{\sf{1\: paise=\frac{1}{100}\:rupee}}}$

The value of 1 rupee coins $\sf{(5x)}$:

$\:\:\:\:\:\implies{\sf{1\times 5x=\underline{5x}}}$

The value of 50 paise coins $\sf{(6x)}$:

$\:\:\:\:\:\implies{\sf{6x\times 5\cancel{0}\times \frac{1}{10\cancel{0}}}}$

$\:\:\:\:\:\implies{\sf{6x\times\frac{5}{10}}}$

$\:\:\:\:\:\implies{\sf{6x\times\frac{1}{2}}}$

$\:\:\:\:\:\implies\underline{\sf{3x}}$

The value of 25 paise coins $\sf{(8x)}$:

$\:\:\:\:\:\implies{\sf{8x\times 25\times \frac{1}{100}}}$

$\:\:\:\:\:\implies{\sf{8x\times\frac{25}{100}}}$

$\:\:\:\:\:\implies{\sf{8x\times\frac{1}{4}}}$

$\:\:\:\:\:\implies\underline{\sf{2x}}$

$\sf{According\:to\:question,}$

$\:\:\:\:\sf{5x+3x+2x=120}$

$\longrightarrow{\sf{10x=120}}$

$\longrightarrow{\sf{x=\frac{12\cancel{0}}{1\cancel{0}}={\underline{\underline{12}}}}}$

$\sf{Therefore,}$

• The number of one rupee coins $\sf{(5x)}$ = $\sf{5\times 12=\red{\underline{60}}}$.
• The number of 50 paise coins $\sf{(6x)}$ = $\sf{6\times 12=\red{\underline{72}}}$.
• The number of 25 paise coins $\sf{(8x)}$=$\sf{8\times 12=\red{\underline{96}}}$.

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