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Mukesh has credit according to which he can buy products at rate of Rs 50 per product. The product is part of overall collection and its value is linked to the number of products that are present in his shop. Mukesh first sells one product at Rs 6, second at Rs 10, third at Rs 14 and so on. If mukesh wants to earn total profit of 20% then what is minimum products he needs to sell. 

Mukesh has credit according to which he can buy products at rate of Rs 50 per product. The product is part of overall collection and its value is linked to the number of products that are present in his shop. Mukesh first sells one product at Rs 6, second at Rs 10, third at Rs 14 and so on. If mukesh wants to earn total profit of 20% then what is minimum products he needs to sell.  Correct Answer 28

Given:

C.P. of price = Rs 50

Profit% = 20%

Formula used:

S.P. = C.P. × (1 + (Profit%/ 100))

Calculation:

C.P. = 50 × N

⇒ S.P. = 6 + 10 + 14 + …… + N terms

⇒ 6 + 10 + 14 + ….. + N terms ≥ 1.2 × 50N

⇒ 2 (3 + 5 + 7…. + N terms) ≥ 60N

⇒ 3 + 5 + 7 + …… + N terms ≥ 30N

Now, 3 + 5 + 7 + …… +  N terms are in arithmetic progression

Tn = a + (N – 1)d

⇒ Tn = 3 + (N -1)2

⇒ Tn = 1 + 2N

⇒ Sn = (N/ 2) × (3 + 1 + 2N)

⇒ Sn = N × (N + 2)

⇒ N × (N + 2) ≥ 30N

⇒ N2 + 2N ≥ 30N

⇒ N2 + 28N ≥ 0

⇒ N ≥ 28

∴ required answer is 28

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