DARE TO SOLVE DAY 7

• • A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
  • Explanation:
    Let us assume he buys n goods.

• • Total CP = 20n

• • Total SP = 2 + 4 + 6 + 8 ….n terms

• • Total SP should be at least 40% more than total CP

• • 2 + 4 + 6 + 8 ….n terms ≥ 1.4 * 20 n

• • 2 (1 + 2 + 3 + ….n terms) ≥ 28n

• • n(n + 1) ≥ 28n

• • n2 + n ≥ 28n

• • n2 – 27n ≥ 0

• • n ≥ 27

• • He should sell a minimum of 27 goods.