Please submit your concern

Question:

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is

Explanation:

Let the number of white and blue shirts bought is 'w' and 'b' respectively.

Total cost price = 1000w + 1125b

⇒ Average cost price/shirt = $\frac{1000\mathrm{w}+1125\mathrm{b}}{\mathrm{w}+\mathrm{b}}$

⇒ Average marked price/shirt = $\frac{1000\mathrm{w}+1125\mathrm{b}}{\mathrm{w}+\mathrm{b}}\times 1.25$

⇒ Average sellingprice/shirt = $\frac{1000\mathrm{w}+1125\mathrm{b}}{\mathrm{w}+\mathrm{b}}\times 1.25\times 0.9$

⇒ Total selling price = (1000w + 1125b) × 1.25 × 0.9

∴ Profit = 51000 = (1000w + 1125b) × 1.25 × 0.9 - (1000w + 1125b)
⇒ 51000 = (1000w + 1125b) × (1.25 × 0.9 - 1)
⇒ 51000 = (1000w + 1125b) × (0.125)
⇒ 1000w + 1125b = 408000
⇒ 40w + 45b = 16320
⇒ 8w + 9b = 3264

w + b will be maximum when we maximum the variable with least coefficiency and minimise the variable with highest coefficient.
Least possible value of of b cannot be 0 as at least one shirt of each type is bought. Hence, the next least possible value of b possible is 8.

∴ b = 8 and w = 399

∴ Highest possible value of w + b = 399 + 8 = 407

Hence, 407.