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A and B started a business with some amount ratio of 2 : 1. After some months they double their share and after 2 months, B leaves the business and C joined the business with an amount Rs. 10000. After 4 months of joining, C doubles his money, and B comes back to the business with his initial principal Rs. 2000. At the end of the year, it is seen that the share of A and C are the same. After how many month A and B double their amount?

A and B started a business with some amount ratio of 2 : 1. After some months they double their share and after 2 months, B leaves the business and C joined the business with an amount Rs. 10000. After 4 months of joining, C doubles his money, and B comes back to the business with his initial principal Rs. 2000. At the end of the year, it is seen that the share of A and C are the same. After how many month A and B double their amount? Correct Answer 4 Months

Given:

A and B started the business with a certain amount at the ratio 2 : 1

After some month they double their money.

After that of 2 months, B leave business and C joined with Rs. 10000

After 4 months of joining C double his money and B back to the business with his initial money Rs. 2000

At the end of the year share of A and C are same.

Concept Used:

Concept of partnership and ratio

Calculation:

At the end of the year share of A and C are same. That means at the end of the year the ratio of the share of A and C will be the same

It is given that B joined the business again with his initial money Rs. 2000 and at the beginning ratio of money of A and B was 2 : 1

That means at the beginning share of A was Rs.4000

Let, after x months A and B Double their money

In x month share of A became 4000x

After x month A double his money and there was no further change

That means the share of A for (12 – x) months is (12 – x) × 8000

Total share of A is {4000x + (12 – x) × 8000}

⇒ (4000x + 12 × 8000 – 8000x)

⇒ (12 × 8000 – 4000x)      ----(1)

C joined the business with Rs. 10000 and continue it for 4 months

After 4 months he doubles his money for the rest of the year

C’s money was Rs. 20000 for

Total share of C is

⇒ (40000 + 120000 – 20000x)

⇒ (160000 – 20000x)      ----(2)

From (1) and (2) get,

(12 × 8000 – 4000x) = (160000 – 20000x)       

⇒ 96000 – 4000x = 160000 – 20000x

⇒ 16000x = 64000

⇒ x = 4

∴ After 4 months A and B double their money.

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