"A piggy bank comprises 5-rupee coins, 10-rupee coins, and 20-rupee coins. The quantity of 5-rupee coins in the piggy bank is 75% more than the number of 20-rupee coins and 30% less than the number of 10-rupee coins. If two coins are randomly drawn from the piggy bank, the probability of drawing a 5-rupee coin and a 10-rupee coin is 1/3. Determine the total number of coins in the piggy bank."

Solution

ATQ, Let the number of 10 rupees coins in the piggy bank be 'p'. So, the number of 5 rupeees coins in the piggy bank = 0.7p And the number of 20 rupees coins in the piggy bank = 0.70/1.75 = 0.4p So, the total number of coins in the piggy bank = p + 0.7p + 0.4p = 2.1p So, the probability that a 5 rupees coins and a 10 rupees coins are drawn = ^pC1 × ^0.7pC1/ ^2.1pC2 = 1/3 (2p × 0.7p) / {2.1p (2.1p - 1) } = 1/3  2.1p - 1 = 2p 0.1p = 1, p = 10 So, the total number of coins in the piggy bank = 2.1 × 10 = 21