Question : A box contains one rupee, fifty paise, and twenty-five paise coins. The total number of coins is 378. The ratio of values of the above coins is 13 : 11 : 7. The number of twenty-five paise coins is:
Option 1: 168
Option 2: 210
Option 3: 132
Option 4: 78
Correct Answer: 168
Solution :
Let the number of one-rupee coins be $x$, the number of 50 paise coins be $y$, and the number of 25 paise coins be $z$.
Given, $x+y+z = 378$------------------(i)
Also $1×x:\frac{50}{100}×y:\frac{25}{100}×z = 13:11:7$
⇒ $x:\frac{y}{2}:\frac{z}{4} = 13:11:7$
Let $x = 13k, y = 22k, z = 28k$
Then, $13k+22k+28k = 378$ (From (i))
⇒ $63k = 378$
⇒ $k = 6$
$\therefore$ The number of 25 paise coins = 28 × 6 = 168
Hence, the correct answer is 168.
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