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Aman started a business investing Rs.$70,000$. Rakhi joined him after six months with an amount of Rs. $1,05,000$ and Sagar joined them with Rs.$1.4$ Lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, $3$ years after Aman started the business?
A.$7:6:10$
B.$12:15:16$
C.$42:45:56$
D.Cannot be determined

Answer
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Hint: We have given that Aman invested Rs.$70,000$ and Rakhi joined him after six months with an amount of Rs.$1,05,000$ and Sagar joined them after another six months with money $1,40,000$. Firstly, we will convert the $3$ year period into months, then we will subtract six months from that time for Rakhi and$12$months from that time period for Sagar. We multiply the time period $36$ months with the amount of $70,000$ time period of $30$ months with $1,05,000$ and $24$ months with $1,40,000$. The ratio of results will give us the profit that should be distributed.

Complete step-by-step answer:
 Amount invested by Aman in business $ = $ Rs.$70,000$
Time period for which he invested the amount $ = 3$ years
$1$ year $ = 12$ months
$3$ years $ = 12 \times 3 = 36$ months
Time period for which Aman invested amount $ = 36$ months
Amount invested by Rakhi in business $ = $ Rs.$1,05,000$
Time period for which Rakhi invested amount $ = 36 - 6$ months
$ = 30$ months
Amount invested by Sagar in business $ = $ Rs.$1,40,000$
Time period for which Sagar invested amount $ = 30 - 6 = 24$ months
The ratio of the amount invested by Aman, Rakhi and Sagar
$ = 70,000:1,05,000:1,40,000$
$ = 70:105:140$
Ratio of the amount after time period
$70 \times 36:105 \times 30:140 \times 24$
$ = 2520:3150:3360$
Dividing by $10$
$252:315:336$
Dividing by $3$
$84:105:112$
Dividing by $7$
$12:15:16$
The amount divided in ratio after time period is $12:15:16$.
So, the profit is also divided in ratio $12:15:16$
Option (B) is correct.

Note: Profit in Maths is considered as the amount gained from any business activity. Basically, when he sells the product more than its cost price, then he gets the profit on it but he has to sell it for less than its cost price, then he has to suffer the loss.