Aptitude 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.**

**Muru**

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**Sravan Reddy**

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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?

Mixture and alligation

**Sravanthi**

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

Pls explain........

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

**D Raja**

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very good refresher for new starter

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