# Easy Ratios & Proportion Solved QuestionAptitude Discussion

 Q. 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:
 ✖ A. 48 ✔ B. 54 ✖ C. 56 ✖ D. 60

Solution:
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),
\begin{align} 10x+10y&=1800\\ 10x+25y&=3690\\ -15y&=1890\\ y&=126 \end{align}

Substitute y value in equation (i)

$x=180–126=54$

Number of 10p coins = 54

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

## (7) Comment(s)

Muru
()

Total no.of coins=180

Take no.of 25 paise coins=x

No.of 10 paise coins=180-x

(25/100)x+(10/100)(180-x)=Rs.36.90

Take 100 as LCM

25x+10(180-x)=3690

25x+1800-10x=3690

15x=3690-1800

15x=1890

x=126

So 10 paise coins=180-x

=180-126

=54

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

Raj
()

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

Prasanth
()

Mixture and alligation

Sravanthi
()

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