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Adrian starts a start-up with a capital of Rs. $85,000.$ Brian joins in the start-up with Rs. $42,500$ after sometime. For how much period does Brian join, if the profits at the end of the year are divided in the ratio of $3:1?$

1. $5$ months
2. $6$ months
3. $7$ months
4. $8$ months

Let Brian time be Y months and given Adrian invested for whole 12 months.

partnership ratio

85000 ×12 : 42500 × y

we need to make this as 3:1 in terms of profit

so

simply dividing by 85000 ×4 on both sides of ratio

we'll now have

3 : y/8

that means Brian invested for 8 months
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