A sum of money is divided among A, B, C and D. The amount received by A and B together is 50% of the amount received by C and D together. C got 140% of the amount received by B and A got 60% of the amount received by B. Find the ratio in which the amount was divided?

A ∶ B ∶ C ∶ D = 2 ∶ 5 ∶ 6 ∶ 8
A ∶ B ∶ C ∶ D = 3 ∶ 5 ∶ 7 ∶ 9
A ∶ B ∶ C ∶ D = 1 ∶ 5 ∶ 7 ∶ 5
A ∶ B ∶ C ∶ D = 3 ∶ 5 ∶ 7 ∶ 17
None of these

LohaHridoy

6 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 2 : A ∶ B ∶ C ∶ D = 3 ∶ 5 ∶ 7 ∶ 9

The amount received by A and B = 50% of the amount received by C and D

⇒ A + B = 1/2(C + D) ---- (I)

⇒ A = 60% of B

⇒ A/B = 3/5

⇒ A ∶ B = 3 ∶ 5 ---- (II)

⇒ C = 140% of B

⇒ C/B = 7/5

⇒ C ∶ B = 7 ∶ 5 ---- (III)

Ratio of A ∶ B ∶ C from (II) and (III)

⇒ A ∶ B ∶ C = 3 ∶ 5 ∶ 7

Let A = 3k, B = 5k and C = 7k

Putting these values in (I)

⇒ (3k + 5k) = ½ × (D + 7k)

⇒ 8k × 2 = D + 7k

⇒ 16k = D + 7k

⇒ D = 9k

∶ Ratio of A ∶ B ∶ C ∶ D = 3 ∶ 5 ∶ 7 ∶ 9

6 views Answered 2022-09-04 04:29

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