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Ramesh and Suresh enter into a partnership with capitals in the ratio of $10:12.$ At the end of $8$ months, Ramesh withdraws. If they receive profits in the ratio of $10:18.$ Find how long Suresh’s capital was used.

  1. $7$ months
  2. $8$ months
  3. $10$ months
  4. $12$ months
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Consider, R (Ramesh) invested 10x and S (Suresh) invested 12x. 

R got 10y back in 8 months and S got 18y back in p months.

8 months -> 10y/10x = y/x returns on investment

1 month -> y/8x return on investment

return amount = duration * returns * investment amount

Therefore, for S - 

18y = p * (y/8x) * 12x

Solving for p, we get p = 12 months.

Answer :- D

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