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- 26. A and B enter into a partnership with capitals in the ratio 2 : 3. At the end of 9 months, A withdraws from the business. If their profits are in the ratio 1 : 2, how long did B invest his capital?

A.12 months

B.8 months

C.10 months

D.14 months

Answer & Explanation

Answer: Option A

Explanation:**Let the initial investment of A and B be Rs. 2x and Rs. 3x respectively.**

Let B invested for a period of y months.

Then, ratio of capitals of A and B

= (2x × 9) : (3x × y) = 1 : 2

=> 18x/(3x × y) = 1/2

=> 6/y = 1/2

=> y = 12

Hence, B's investment is for 12 months.

Let B invested for a period of y months.

Then, ratio of capitals of A and B

= (2x × 9) : (3x × y) = 1 : 2

=> 18x/(3x × y) = 1/2

=> 6/y = 1/2

=> y = 12

Hence, B's investment is for 12 months.

- 27. A, B and C started a business with a total investment of Rs. 72000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find A's share.

A.Rs. 3240

B.Rs. 2520

C.Rs. 2880

D.Rs. 3360

Answer & Explanation

Answer: Option A

Explanation:**Let C's investment = Rs. x**

B's investment = Rs. (x - 3000)

A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)

Now, (A + B + C)'s investment = Rs. 72000

=> x + (x - 3000) + (x + 3000) = 72000

=> 3x = 72000

=> x = 24000

Hence, A's investment = Rs. 27000

B's investment = Rs. 21000

C's investment = Rs. 24000

Ratio of the capitals of A, B and C

= 27000 : 21000 : 24000

= 9 : 7 : 8

A's share = Rs. [(9/24) × 8640] = Rs. 3240

B's investment = Rs. (x - 3000)

A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)

Now, (A + B + C)'s investment = Rs. 72000

=> x + (x - 3000) + (x + 3000) = 72000

=> 3x = 72000

=> x = 24000

Hence, A's investment = Rs. 27000

B's investment = Rs. 21000

C's investment = Rs. 24000

Ratio of the capitals of A, B and C

= 27000 : 21000 : 24000

= 9 : 7 : 8

A's share = Rs. [(9/24) × 8640] = Rs. 3240

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