It was intended that Rs. 585 be divided among P, Q and R in the ratio of 4: 3: 2, but by mistake the distribution was made in the proportion of 1/4 : 1/3 : 1/2. How much does ‘R’ gain by the error?
Question
It was intended that Rs. 585 be divided among P, Q and R in the ratio of 4: 3: 2, but by mistake the distribution was made in the proportion of 1/4 : 1/3 : 1/2. How much does ‘R’ gain by the error?
Solution
Sure, let's solve this step by step.
Step 1: Calculate the total ratio The total ratio is 4:3:2, which adds up to 4+3+2 = 9.
Step 2: Calculate the original share of 'R' 'R' was supposed to get 2 parts of the total 9 parts. So, the original share of 'R' would be (2/9)*585 = Rs. 130.
Step 3: Calculate the mistaken share of 'R' The mistaken ratio was 1/4 : 1/3 : 1/2. The total of this ratio is 1/4 + 1/3 + 1/2 = 1.08333. So, 'R' got (1/2)/1.08333 of the total amount, which is Rs. 270.
Step 4: Calculate the gain of 'R' The gain of 'R' is the mistaken share minus the original share, which is Rs. 270 - Rs. 130 = Rs. 140.
So, 'R' gained Rs. 140 by the error.
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