P, Q and R entered into a partnership with an investment of Rs.4500, Rs.6000 and Rs.5000 respectively and after x months, P increased its investment by 20% and Q withdrew Rs.1000 from its investment and at the end of one year, the ratio of the profit obtained by P, Q and R is 72:85:75. Find the value of x.
a) 6
b) 4
c) 9
d) 8
e) None of these
Sol:
Profit ratio of P, Q and R = (4500 * x) + (4500 *
120/100 * (12 – x)) : (6000 * x) + (5000 * (12 – x))
: (5000 * 12) = 4500x + 5400 * (12 – x) : 6000x +
60000 – 5000x : 60000 = (4500x + 64800 –
5400x) : (1000x + 60000) : (60000) = (64800 –
900x) : (1000x + 60000) : 60000
(64800 – 900x)/(60000) = 72/75
(648 – 9x)/600 = 24/25
16200 – 225x = 14400
1800 = 225x
x = 8
