Rs. 535 is divided among A, B and C so that if Rs. 15, Rs. 10, Rs. 30 be subtracted from their respective shares, the remainder may be in the ratio 4:5:7. What were their initial shares (in Rs.) ?

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135, 160, 240

160, 280, 318

150, 210, 325

None of these

answer is A.

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Detailed Solution

Concept: Set up the proportion and solve it based on the given and unknown ratios. Take any variable as the reference number while answering these ratio questions. Simplify the word assertions to achieve the desired result by converting them into mathematical expressions.
Given that Rs. 535 is divided among A, B, and C, and that the remainders may be in the ratio

if Rs. 15, Rs. 10, and Rs. 30 are deducted from each of their respective shares, let's assume that "x" is the term that all three A, B, and C share.
Remainders are in the ratio

after subtraction (given)
Let A continue with the amount

and B continue with the amount

Let C continue with an amount of

.
Additionally, the total of ratios equals the balance remaining after deducting Rs. 535 from Rs. 15, Rs. 10, Rs. 30,
Question Image

The initial shares that A received are now

.
Put the "X" value there.
Consequently, the first shares that A received are
Question Image

Consequently, B's first share allocation is
Question Image

Consequently, C's first share allocation is
Question Image

The needed solution is that the initial shares of A, B, and C were Rs. 135, Rs. 160, and Rs. 240, based on equations (1) , (2) , and (3) .
Hence, the correct answer is option 1) 135, 160, 240

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