At the beginning of a year, Arum and Ajoy jointly started and business investing Rs. 24000 and Rs. 30000 respectively. But after new months Arum invested Rs. 12000 more in the business. If the profit of the business be Rs. 14030 at the end of the year and Arun got Rs. 7130 as the profit, then find the number of month after which Arum had invested more in the business.

Explanation

Let Arum invested Rs. 12000 more after `x` months.
So the capital of Arum with respect of 1 month
`=Rs. (24000xx x+(24000+12000)(12-x))`
`=Rs. (24000x+432000-36000x)`
`=Rs. (432000-12000x)`
`=Rs. (12000(36-x))`
Also the capital of Ajoy with respect of 1 month `=Rs. 30000xx12=Rs. 360000`
Total profit `=Rs. 14030`
Arun's `=Rs. 7130`
`:.` Ajoy's `=Rs. (14030-7130)=Rs. 6900`
Now (Arun's profit): (Ajoy's profit)`=7130:6900=31:30`
We know that ratio of captal `=` ratio of profit
So `12000(36-x):360000=31:30`
`implies(12000(36-x))/360000=31/30`
`implies(36-x)/30=31/30implies36-x=31impliesx=36-31`
`impliesx=5`
Hence Arun had invested Rs. 12000 more after 5 months of the starting of the business.