A, B and C entered into a partnership with the capital of Rs. 60,000/- , Rs. 50,000/- and Rs.70,000/- resp. If C joins x months after starting of the year and A leaves them y month before end of the year then they share the profit in the ratio of 18 : 20 : 21. Find the value of x and y.

3 & 3

               A    :     B     :     C

Profit :   18   :    20    :     21

Invs. :     6   :     5     :       7

Time:      3    :     4     :      3         .............(i)

B invest for 12 months, therefore, (i) multiply by 3

Time:      9    :     12   :      9

Now,

C invest for 9 months out of 12 months, it means C join the business 3 months after the starting.

Hence, x = 3 and

A invest for 9 months out of 12 months, it means A leaves them 3 months before the end of the year.

Hence, y = 3