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A solution of ghee and sugar syrup contains 45% ghee. A process when applied decreases the quantity of ghee by one-eighth and the quantity of sugar syrup by one-fifth, each time it is applied. What is the minimum number(approx.) of times that the process must be applied so that the solution would have more ghee than sugar syrup?

A solution of ghee and sugar syrup contains 45% ghee. A process when applied decreases the quantity of ghee by one-eighth and the quantity of sugar syrup by one-fifth, each time it is applied. What is the minimum number(approx.) of times that the process must be applied so that the solution would have more ghee than sugar syrup? Correct Answer 3

Let the process be applied ‘n’ times.

Initial ratio of ghee and sugar syrup = 45 / 55 = 9 / 11

Ratio of ghee and sugar syrup after the process is applied n times

⇒ {9(1 - (1 / 8))n} / {11(1 - (1 / 5))n} = (9 / 11)

As the solution must have more ghee than sugar syrup after the process is applied n times, this ratio is more than one.

⇒ (9 / 11) > 1

⇒ (35 / 32)n > 11 / 9

⇒ 11 / 9 = 1.22

⇒ (35 / 32)1 = 1.09

⇒ (35 / 32)2 = 1.196

⇒ (35 / 32)3 = 1.308

Thus, minimum value of n is 3(approx.). 

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