Question

man sells his goods at 25% p had he purchased it for x less and sold for x less then he gains 5 % more. had he buy it for y less and sold it for y less then he gains 40%. what is the profit % if both cp and sp are reduced by rs (x+y)
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Answer 1

• The profit % if both CP and SP are reduced by Rs.(x + y) is equal to 54.54% .

Given :- A man sells his goods at 25% profit . Had he purchased it for x less and sold for x less then he gains 5 % more. Had he buy it for y less and sold it for y less then he gains 40%.

To Find :- What is the profit % if both CP and SP are reduced by Rs.(x + y) ?

Formula used :-

• SP = {CP × (100 + Profit %)}/100
• Profit % = (Profit in Rs. × 100) / CP
• CP = Cost Price
• SP = Selling Price

Solution :-

Let CP of the good was Rs. 100a .

So,

→ CP = Rs. 100a

→ Profit = 25%

→ SP = (100a × 125)/100 = Rs. 125a

Case 1) :- when CP and SP are reduced by Rs. x.

→ New CP = Rs.(100a - x)

→ New SP = Rs.(125a - x)

→ New profit = (125a - x) - (100a - x) = Rs.25a

A/q,

→ 30 = (25a * 100)/(100a - x)

→ 3(100a - x) = 250a

→ 300a - 3x = 250a

→ 3x = 50a

→ x = Rs.(50a/3) ---- (1)

Case 2) :- when CP and SP are reduced by Rs. y.

→ New CP = Rs.(100a - y)

→ New SP = Rs.(125a - y)

→ New profit = (125a - y) - (100a - y) = Rs. 25a

A/q,

→ 40 = (25a * 100)/(100a - y)

→ 4(100a - y) = 250a

→ 400a - 4y = 250a

→ 4y = 150a

→ y = Rs. (75a/2) ---- (2)

adding (1) and (2) :-

→ (x + y) = (50a/3) + (75a/2)

→ (x + y) = (100a + 225a)/6

→ (x + y) = Rs. (325a/6)

Then,

→ New CP = 100a - (325a/6) = (275a/6)

→ New SP = 125a - (325a/6) = (425a/6)

→ New profit = (425a/6) - (275a/6) = (150a/6) = Rs. 25a

therefore,

→ Required profit % = (Profit × 100)/CP

→ Required profit % = (25a * 100 * 6)/275a

→ Required profit % = (600/11)

→ Required profit % = 54.54% (Ans.)

Hence, Required profit % is equal to 54.54% .

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