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Q.

A, B and C entering into a partnership by investing in the ratio 3:2:4. After one year, B invests another Rs 2,70,000 and C at the end of 2 years also invests Rs 2,70,000. At the end three years, profit is shared in the ratio of 3:4:5. Find the initial investment of C.

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a

Rs . 2, 70, 000

b

Rs 1, 80, 000

c

Rs 3, 60, 000

d

None of these

answer is C.

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Detailed Solution

Concept- For converting the ratio of initial investments of A,B and C into rupees we will be multiplying this ratio 3:2:4 by x so the investment of A, Band c are 3x,2x,and 4x respectively. Now we will use this natal investment to calculate the profit share A,B and C and equate it to 2:4:5. After solving this equation we can calculate the value of x and then substitute this value of x in 4 x we will get the initial investment of C.
initial investment of

A = 3 x

initial investments of

B = 2 x

initial investment of

c = 4 x

Share of A at the end of three years =

3 x 3 = 9 x

Share of B at the end of three years

= 2 x + 2, 70, 0002

= 2 x + 2 x + 2, 70, 0002

= 6 x + 5, 40, 000

Share of C at the end of three years

= 4 x^{2} + 4 x + 2, 70, 000

= 8 x + 4 x + 2, 70, 000

= 12 x + 2, 70, 000

Ratio of share A ,B and c at the end of three years :

= 9 x : (6 x + 5, 40, 000) : (12 x + 2, 70, 000)

To makes this ratio equal 3:4:5 we are dividing the above ratio by 3 x

3 : (\frac{6 x + 5, 40, 000}{3 x}) : (\frac{2 x + 2, 70, 000}{3 x})

Above ratio s equal to 3:4:5
so comparing the above ratio by 3:4:5 we get

\frac{6 x + 5, 40, 000}{3 x} to 4

4 = \frac{6 x + 5, 40, 000}{3 x}

Cross multiplying the above equation

12 x = 6 x + 5, 40, 000

6 x = 5, 40, 000

Dividing 6 on both sides we get

x = \frac{5, 40, 000}{6}

x = 90, 000

Get the initial investments of C we are going to substitute the above value of x is 4x

= 4 (90, 000)

=

3, 60, 000

The initial investments of C is Rs. 3,60,000
Hence, option 3 is correct.

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