Question

Rahul has a box which contains 25 paise, 50 paise and ₹1 coins. If the ratio of number of coins of 25 paise and 50 paise is 4 : 5 respectively, the number of ₹1 coins is 60 and he has ₹95 in his box, then the probability of selecting a 50 paise coin is

• A. $\frac{1}{2}$
  
• B. $\frac{1}{3}$
  
• C. $\frac{2}{3}$
  
• D. $\frac{3}{5}$
  

Answer 1

The correct option is B $\frac{1}{3}$


Given that the ratio of the number of coins of 25 paise and 50 paise is 4 : 5 respectively.
Let the number of coins of 25 paise and 50 paise be 4x and 5x respectively, where x is any natural number.
$\therefore \text{Total sum of money}$
$=4x\times 0.25+5x\times 0.50+60\times 1$
= ₹(x + 2.5x + 60)
= ₹(3.5x + 60)
$\Rightarrow 3.5x+60=95$ $(\because \text{Total money}=₹95)$
$\Rightarrow 3.5x=35$
$\Rightarrow x=10$
$\therefore \text{Number of 50 paise coins}=5\times 10$
$=50$
$\text{Number of 25 paise coins}=4\times 10$
$=40$
Total number of coins = 50 + 40 + 60 = 150
$\therefore \text{P(selecting a 50 paise coin)}=\frac{\text{Number of 50 paise coins}}{\text{Total number of coins}}$
$=\frac{50}{150}$
$=\frac{1}{3}$
Hence, the correct answer is option (b).