If ₹ R are divided between ‘A’ and ‘B’ in the ratio of a/b : c/d, then what is…
2025
If ₹ R are divided between ‘A’ and ‘B’ in the ratio of a/b : c/d, then what is the amount that A shall receive ?
- A.
adR/(ad + bc)
- B.
abR/(ad + bc)
- C.
abR/(ac + bd)
- D.
adR/(ab + cd)
Attempted by 20 students.
Show answer & explanation
Correct answer: A
Concept: When a total amount is split in a ratio written as fractions, a/b : c/d, the fractional ratio is first converted into a whole-number ratio by multiplying every term by a common multiple of the two denominators (here, simply their product, bd). Once the ratio is a whole-number ratio m : n, a total R divided in that ratio gives the first party a share of R × m/(m + n).
Given ratio: a/b : c/d.
Multiply every term by bd to clear both denominators: (a/b) × bd : (c/d) × bd = ad : bc.
So A's share : B's share = ad : bc.
Total number of parts = ad + bc.
A's share = R × [ad / (ad + bc)] = adR / (ad + bc).
Cross-check: pick simple values, say a = 1, b = 2, c = 1, d = 3, so the ratio is 1/2 : 1/3. Multiplying every term by bd = 6 gives 3 : 2, so A's share should be (3/5)R. Substituting the same values into adR/(ad + bc) gives ad = 1×3 = 3 and bc = 2×1 = 2, so the share is 3R/(3+2) = 3R/5 — the two methods agree, confirming adR/(ad + bc) as the correctly derived share.