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Explanation:

Cost price of each item is Rs. 20 while their selling price are Rs. 2, 4, 6 and so on. If minimum profit percentage earned by selling these items is 40%, what is the minimum number of items?

Let the total number of items = n

Total cost priceof these items = 20n

Now, selling price of 1st item is 2, 2nd item is 4, 3rd item is 6 and so on hence, nth item will be sold at 2n.
∴ Selling  price of these items = 2 + 4 + 6 + ... + 2n
= 2(1 + 2 + 3 + ... + n)
= n(n + 1)

Since 40% profit is earned 
​​​​​​​⇒ Total Selling Price = Total Cost Price × 1.4
​​​​​​​⇒ n(n + 1) = 20n × 1.4
​​​​​​​⇒ (n + 1) = 20 × 1.4
⇒ n + 1 = 28
⇒ n = 27

Hence, option (c).