Question

(3)
88. किसी थैले में 90 रुपये की राशि 50 पैसे, 25 पैसे और
10 पैसे के सिक्कों के रूप में हैं। यदि 50 पैसे, 25 पैसे
और 10 पैसे के सिक्कों का अनुपात 2 : 3:5 है, तो
थैले में 25 पैसे के सिक्कों की संख्या क्या है ?
(1) 80
(2) 120
(3) 100
(4) 135
ISSC Graduate Level, 2003)​

Answer 1

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$\large \underline \bold{Given}$:-

The ratios of the coins of 50 paise ,

25 paise and 10 paise = 2 : 3 : 5

Sum of all types of coins as 50 paise , 25 paise and 10 paise is 90 rupees.

$\large \underline \bold{To \: Find}$:-

Calculate the no. of coins of 25 paise in the beg ?

$\large \underline \bold{Solution}$:-

$\small \underline \bold{Let}$-

the coins of 50 paise , 25 paise and 10 paise are $\sf \frac{2x}{2}$ , $\sf \frac{3x}{4}$ and $\sf \frac{5x}{10}$.

As we Given -

the sum of all coins is 90 Rs.

according to the question -

➯ $\sf \: \: \: \dfrac{\cancel{2}x}{\cancel{2}} + \dfrac{3x}{4} + \dfrac{\cancel{5}x}{\cancel{10}} \: = \: 90$

➯ $\sf \: \: \: \: x \: + \: \dfrac{3x}{4} \: + \: \dfrac{x}{2} \: \: = \: \: 90$

➯ $\sf \: \: \dfrac{4x}{4} + \dfrac{3x}{4} + \dfrac{2x}{4} \: \: = \: \: 90$

➯ $\sf \dfrac{(4x + 3x + 2x)}{4} \: \: = \: \: 90$

➯ $\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dfrac{\cancel{9}x}{4} \: \: = \: \: \cancel{90} \: \: 10$

➯ $\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dfrac{x}{4} \: \: = \: \: 10$

➯ $\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x \: = \: 4\times 10$

➯ $\small \bold{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x \: \: = \: \: 40}$

Now ,

$\sf The \: Coins \: of \: 50 \: paise \: = \: 2\times 40 \: = \: 80$

$\sf The \: coins \: of \: 25 \: paise \: = \: 3\times 40 \: = \: 120$

$\sf The \: coins \: of \: 10 \: paise \: = \: 5\times 40 \: = \: 200$

$\small \bold{There \: are \: 120 \: coins \: of \: 25 \: paise.}$

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Answer 2

$\huge{\underline{\red{\mathfrak{♡Answer♡}}}}$

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$\large \underline\bold\orange{Given}$

The ratios of the coins of 50 paise ,

25 paise and 10 paise = 2 : 3 : 5

Sum of all types of coins as 50 paise , 25 paise and 10 paise is 90 rupees.

$\large \underline\bold\orange{To \: Find}$

Calculate the no. of coins of 25 paise in the beg ?

$\large\underline\bold\orange{Solution}$

$\underline\bold\orange{Let}$

the coins of 50 paise , 25 paise and 10 paise are$\sf \frac{2x}{2}, \sf \frac{3x}{4} and \sf \frac{5x}{10}$

As we Given -

the sum of all coins is 90 Rs. according to the question -

$\implies \sf {\dfrac{\cancel{2}x}{\cancel{2}} + \dfrac{3x}{4} + \dfrac{\cancel{5}x}{\cancel{10}} \: = \: 90}$

$\implies\sf {x \: + \: \dfrac{3x}{4} \: + \: \dfrac{x}{2} \: \: = \: \: 90}$

$\implies \sf {\dfrac{4x}{4} + \dfrac{3x}{4} + \dfrac{2x}{4} \: \: = \: \: 90}$

$\implies\sf{\frac{(4x + 3x + 2x)}{4} \: \: = \: \: 90}}$

$\implies\sf{\dfrac{\cancel{9}x}{4} \: \: = \: \: \cancel{90} \: \: 10}$

$\implies\sf{\dfrac{x}{4} \: \: = \: \: 10}$

$\implies\sf{ x \: = \: 4\times 10}$

$\implies \small \bold{x = \: \: 40}$

Now ,

$\implies\sf {The \: Coins \: of \: 50 \: paise \: = \: 2\times 40 \: = \: 80}$

$\implies\sf {The \: coins \: of \: 25 \: paise \: = \: 3\times 40 \: = \: 120}$

$\implies\sf {The \: coins \: of \: 10 \: paise \: = \: 5\times 40 \: = \: 200}$

$\large\bold\purple{There \: are \: 120 \: coins \: of \: 25 \: paise.}$

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