A bag contains 50 paise, 1 rupee and 2-rupee coins in the ratio of 2:3:4. If the total amount is Rs.240, what is the total number of coins? A.210 B.180 C.270 D.171
Hint: First use the ratio given to assume the number of each coin in a single variable and then use the given total to find the number of coins.
Complete step-by-step answer: Given, a bag contains 50 paise, 1 rupee and 2-rupee coins in the ratio of 2:3:4 such that the total sum of the value of coins is Rs.240. Using the ratio given, let us make an assumption of the number of coins. Let the number of 50 paise coins be $2x$, 1-rupee coins be $3x$ and 2-rupee coins be $4x$. The total value of the coins is given to be Rs.240. Also, we know that 1 rupee = 100 paise, $ \Rightarrow $50 paise = 0.5 rupees Equating the total value calculated using given ratio to Rs.240, we get $ 240 = 2x \times 0.5 + 3x \times 1 + 4x \times 2 \\ \Rightarrow 240 = 12x \\ \Rightarrow x = 20 \\ $ Using the above obtained value of x, we can determine the count of each individual coin in the bag. $ \Rightarrow $Total number of 50 paise coins $ = 2x = 40$ $ \Rightarrow $Total number of 1-rupee coins $ = 3x = 60$ $ \Rightarrow $Total number of 2-rupee coins $ = 4x = 80$ Hence total number of coins $ = 60 + 40 + 80 = 180$ Therefore, option (B). 180 is the correct answer.
Note: Problems like above should be solved by using the ratio to form the equation in a single variable. The unit should be kept in mind while using the ratio to calculate quantities as it should be same