A insulin producing company starts the production with 4 kg of insulin, the next day the amount of insulin was increased to 12 kg. If the amount of insulin on the n + 1th day : amount of insulin on nth day ∷ amount of insulin on nth day : amount of insulin on the n – 1th day and once the amount of insulin crosses 100 kg, 90 kgs of the insulin is removed. What will be the total production of insulin in 23 days?

A insulin producing company starts the production with 4 kg of insulin, the next day the amount of insulin was increased to 12 kg. If the amount of insulin on the n + 1th day : amount of insulin on nth day ∷ amount of insulin on nth day : amount of insulin on the n – 1th day and once the amount of insulin crosses 100 kg, 90 kgs of the insulin is removed. What will be the total production of insulin in 23 days? Correct Answer 1800 kg

Amount of insulin on first day = 4

Amount of insulin on second day = 12

Amount of insulin on the n + 1^th day: amount of insulin on n^th day ∷ amount of insulin on n^th day: amount of insulin on the n – 1^th day

⇒ amount of insulin on the 3^rd day: amount of insulin on 2^nd day ∷ amount of insulin on 2^nd day: amount of insulin on the 1^st day

⇒ Amount of insulin on the 3^rd day = Amount insulin on 2^nd day × Amount of insulin on 2^nd day/Amount of insulin on 1^st day

⇒ Amount of insulin on the 3^rd day = 12 × 12/4 = 36

The amount of insulin triples every day.

⇒ 1^st day = 4

⇒ 2^nd day = 12

⇒ 3^rd day = 36

⇒ 4^th day = 108, 90 kgs will be removed and remaining 18 kgs will be left for further production

⇒ 5^th day = 54

⇒ 6^th day = 162, 90 kgs will be removed and remaining 72 kgs will be left for further production

⇒ 7^th day = 216, 90 kgs will be removed and remaining 126 kgs will be left, it is still more than 100, so 90 kgs will be removed again. So, 180 kgs removed and 36 kgs will be left for further production.

For first 7 days the production will be 90 + 90 + 180 = 360 kgs and the 36 kg will be left for production.

Once 36 kgs is left, every 4 days the cycle repeats and production per cycle = 360

⇒ In 23 days, initial 7 days and 4 cycles are there.