Question : In a wallet, there are coins of Re. 1, Rs. 2 and Rs. 5 in the ratio of 2 : 5 : 3 respectively. If there is Rs. 54 in all, then how many Rs. 5 coins are there?
Option 1: 20
Option 2: 10
Option 3: 4
Option 4: 6
Correct Answer: 6
Solution :
Let the number of Re. 1, Rs. 2, and Rs. 5 coins as \(x\), \(y\), and \(z\) respectively.
Given that these are in the ratio 2 : 5 : 3, we can express them as \(x = 2k\), \(y = 5k\), and \(z = 3k\) for some constant \(k\).
The total value of all coins is Rs. 54.
$⇒1 \times x + 2 \times y + 5 \times z = 54$
Substituting the expressions for \(x\), \(y\), and \(z\) in terms of \(k\) into this equation gives:
$⇒1 \times (2k) + 2 \times (5k) + 5 \times (3k) = 54$
$⇒k = 2$
Substituting \(k = 2\) into the expression for \(z\) gives \(z = 3 \times 2 = 6\)
Hence, the correct answer is 6.
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