A plywood factory sells plywood to a dealer earning a profit of 16%. The dealer further sells it to a shopkeeper earning a profit of 25%. When the manufacturing cost of the plywood increased by 25%, the factory again took its profit by 25%, and the dealer took his profit by 12%. If the shopkeeper has to pay Rs. 4230 more for the plywood, what is the new manufacturing cost of plywood?

A plywood factory sells plywood to a dealer earning a profit of 16%. The dealer further sells it to a shopkeeper earning a profit of 25%. When the manufacturing cost of the plywood increased by 25%, the factory again took its profit by 25%, and the dealer took his profit by 12%. If the shopkeeper has to pay Rs. 4230 more for the plywood, what is the new manufacturing cost of plywood? Correct Answer Rs. 17625

Formula Used:

When two successive profits of p% and q% are earned on a product, overall profit = (p + q + pq/100)%

Calculation:

Let the initial manufacturing cost of plywood be Rs. ‘x’

When the plywood is successively sold twice earning profit of 16% and 25%,

⇒ Overall profit% = 16 + 25 + 400/100 = 45%

⇒ Price paid by shopkeeper = x + 45% of x = 1.45x

Now,

When the manufacturing cost increased by 25%,

⇒ New manufacturing cost = 125% of x = 1.25x

⇒ New profit% of factory = 125% of 1.25x = 1.5626x

⇒ New profit% of dealer = 112% of 1.5626x = 1.75x

But, the shopkeeper had to pay Rs. 4230 more,

⇒ 1.75x - 1.45x = 4230

⇒ x = 4230/0.30 = Rs. 14100