Ratios & Proportion

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A sum of Rs. 36.90 is made up of 180 coins which are either 10 paise coins or 25 p coins. The number of 10 p coins is:









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Option(B) is correct

Step (i) Total number of coins = 180

Let $x$ be number of $10p$ coins and $y$ be number of $25p$ coins

\(x+y=180\) --------(i)

Step (ii) Given 10p coins and 25p coins make the sum = Rs. 36.90 

\(\begin{align*} \dfrac{10x}{100}+\dfrac{25y}{100}&=36.9\\ \Rightarrow 10x+25y&=3690 \end{align*}\)-----(ii)

Step (iii) 

Solving (i) and (ii),
Answer image for Ratios & Proportion, Aptitude:1015-1\(\begin{align} 10x+10y&=1800\\ 10x+25y&=3690\\ -15y&=1890\\ y&=126 \end{align}\)

Substitute y value in equation (i)


Number of 10p coins = 54

Edit: For an alternative solution, check comment by Sravan Reddy.

(5) Comment(s)

Sravan Reddy

If all were 10 paise coins - total value = 18

If all were 25 paise coins - total value = 45

Current value is 36.9 which splits 18 and 45 as 18.9:8.1 = 7:3

So 10 paise coins are $\dfrac{3}{(7+3)} * 180 = \text{54 coins}$


Please explain the third step. How 36.9 splits 18 and 45?


In second step why did they take denominator as a 100 for both x and y.
Pls explain........

Purnima Bamola

bcz we have to 10 paise and 25 paise into Rs so, we will divide by 100 both paise

D Raja

very good refresher for new starter