Question

An amount of Rs 735 was divided between A, B and C. If each of them had received Rs 25 less, their share would have been in the ratio 1 : 3 : 2. The money received by C was
(a) Rs 195
(b) Rs 200
(c) Rs 225
(d) Rs 245

Answer 1

Hint: First of all, we will assign variables to the money received by A, B and C. We know that the sum of the money received by A, B and C is 735. Moreover, we know that to deduct 25 from each of their money, the money left with each will be in the ratio 1 : 3 : 2. From the given relations, we will find the amount of money received by C.

Complete step-by-step answer:
Let a be the amount of money received by A, b be the amount of money received by B and c is the amount received by C.
Thus, we know that a + b + c = 735.
Now, it is given that if 25 is reduced from each of their shares, the amount of money left with them will be in the ratio 1 : 3 : 2.
It is to be noted that if 25 is reduced from each of their money, the sum of the amounts of money held by A, B and C will be 25(3) less than the sum of the amounts of money they had initially.
Thus, the money left with A will be (a – 25), money left with B will be (b – 25) and money left with C is (c – 25).
And (a – 25) + (b – 25) + (c – 25) = 735 – 25(3)
 $ \Rightarrow $ (a – 25) + (b – 25) + (c – 25) = 735 – 75
 $ \Rightarrow $ (a – 25) + (b – 25) + (c – 25) = 660
And, the ratio of the amount left with them is 1 : 3 : 2.
 $ \Rightarrow $ (a – 25) : (b – 25) : (c – 25) = 1 : 3 : 2
Let K be the constant of proportionality.
Thus, amount left with A will be K, amount left with B will be 3K and amount left with C is 2K.
Also, K + 3K + 2K = 660
 $ \Rightarrow $ 6K = 660
 $ \Rightarrow $ K = 110
Thus, amount left with A is K = 110
 $ \Rightarrow $ a – 25 = 110
Similarly, amount left with B is 3K = 330
 $ \Rightarrow $ b – 25 = 330
And amount left with C is 2K = 220
 $ \Rightarrow $ c – 25 = 220
 $ \Rightarrow $ c = 245
Therefore, the original amount of money received by C is c = Rs 245.
Hence, option (d) is the correct option.

Note: Students have to apply simple logic that if an equal amount is deducted from each of the parts, the sum of the deducted amount will be reduced from the total. Moreover, this question requires basic knowledge of ratios. Students are advised to be thorough with the concepts.