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The following question has three statements. Study the question and the statements and decide which of the statement (s) is/are necessary to answer the question. A, B and C are partners in a partnership firm. C got retired and his sons D and E are admitted as partners in the firm. In what ratio the profit will be shared between A, B, D and E? I) D’s and E’s share in the profit is in the ratio 3 ∶ 5 II) Ratio of A, B and C was 1 ∶ 2 ∶ 3 III) A’s share is double than E’s share and B receives Rs. 10500 out of total profit of Rs. 37500.

The following question has three statements. Study the question and the statements and decide which of the statement (s) is/are necessary to answer the question. A, B and C are partners in a partnership firm. C got retired and his sons D and E are admitted as partners in the firm. In what ratio the profit will be shared between A, B, D and E? I) D’s and E’s share in the profit is in the ratio 3 ∶ 5 II) Ratio of A, B and C was 1 ∶ 2 ∶ 3 III) A’s share is double than E’s share and B receives Rs. 10500 out of total profit of Rs. 37500. Correct Answer I and III together

Considering Statement I,

Ratio of D and E is 3 ∶ 5

Hence, this statement is not sufficient alone

Considering Statement II,

Old ratio = 1 ∶ 2 ∶ 3

Old ratio has nothing to do with new ratio as sacrifice and gains of partner are not given

Hence, this statement is not sufficient alone

Considering Statement III,

Ratio of A and E is 2 ∶ 1

B’s share = 10500/37500 = 7/25

Hence, this statement is not sufficient alone

Considering Statement I and III together,

I. D’s and E’s share is in ratio 3 ∶ 5

III. A’s share is double than E’s share and B receives Rs. 10500 out of total profit of Rs. 37500

Le the E’s share be x

From III, A’s share will be 2x

From I, D’s share will be 3x/5

Fom III, B’s share = 10500/37500 = 7/25

It means that share of A, D and E jointly is 1 - (7/25)

⇒ 18/25

So, 2x + (3x/5) + x = 18/25

Taking 5 as LCM,

⇒ (10x + 3x + 5x)/5 = 18/25

⇒ 18x/5 = 18/25

Using cross multiplication method,

⇒ 450x = 90

⇒ x = 90/450

⇒ x = 1/5

E’s share is 1/5

A’s share is 2/5

D’s share is 3/25

New ratio of A, B, D and E = 2/5 ∶ 7/25 ∶ 3/25 ∶ 1/5

i.e. Ratio = 10 ∶ 7 ∶ 3 ∶ 5

∴ The statements I and III are required to answer the question

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