Satish, Bhavya and Abhishek entered into a partnership with Rs 16000, Rs 20000 and Rs 24000 respectively. Abhishek joined them after (x) months and Bhavya left (x) month before the end of year. If they share profit at the end of the year. If they share profit in the ratio 48 : 35 : 30 . Find the value of (x) ?

Partnership profit ratio = Investment × Time. Satish: 16000 × 12 = 192000. Bhavya: 20000 × (12 - x) = 20000(12 - x). Abhishek: 24000 × x. Ratio = 192000 : 20000(12 - x) : 24000x = 48 : 35 : 30. Simplifying by 1000: 192 : 20(12 - x) : 24x = 48 : 35 : 30. This gives 192/(24x) = 48/30, so 192/x = 48/30 × 24 = 38.4, x = 192/38.4 = 5. Or: 20(12 - x)/24x = 35/30, so (240 - 20x)/24x = 7/6, 6(240 - 20x) = 168x, 1440 - 120x = 168x, 1440 = 288x, x = 5.