Find Profit & Cost Price

Q. If an article is sold for ₹144 and the profit % = Cost Price, find the Cost Price (C.P.).


Shortcut: Trick: Take two factors of 144 whose difference is 10. Then, attach a zero to the smaller factor.


Check: 144 = 18 * 8 (Difference18 - 8 = 10)


Ans: C.P. = ₹80


Q. If an article is sold for ₹21 and the loss % = Cost Price, find the Cost Price (C.P.).


Shortcut: Trick: Take two factors of 21 whose sum is 10. Then, attach a zero to the smaller factor.


Check: 21 = 7 * 3 (Sum 7 + 3 = 10)


Ans: C.P. = ₹30


@. Simple Interest – Super Short Tricks : Link 1 : Link 2 


Q. If an article is sold for ₹75 and the profit % = Cost Price, find the Cost Price (C.P.).


Shortcut method: Trick: Take two factors of 75 whose subtraction is 10. Then, attach a zero to the smaller factor.


Check: 75 = 15 * 5 = (Difference15 - 5 = 10)


Ans: C.P. = ₹50


Q: A man buys 8 pens for ₹1. How many pens should he sell for ₹1 to make a 60% profit?
Solution:
Cost per pen = ₹1 / 8 = ₹0.125.
To get 60% profit, selling price per pen = 0.125 × 1.6 = ₹0.20.
Number of pens he must sell for ₹1 = 1 / 0.20 = 5 pens.
Ans: 5


Q: 1160 chairs are bought for ₹24,560. How many chairs must be sold for ₹24,560 to earn 20% profit?
Solution:
Let cost per chair = ₹24,560 ÷ 1160.
If x chairs cost = CP_x, to have 20% profit: selling price = 1.2 × CP_x.


Here selling price (given) = ₹24,560.
So 24,560 = 1.2 × x × (24,560/1160)
Simplify x = 1160/1.2 = 1160 × 5/6 = 966 2/3.
That is not a whole chair. Practically:



  • To get at least 20% profit sell 966 chairs (gives ≈20.08% profit).

  • Selling 967 chairs gives ≈19.96% (just under 20%).
    Exact mathematical answer: 9662/3​ chairs.
    Practical answer: 966 chairs to exceed 20% profit (967 gives slightly less than 20%).


Q: A person loses 20% by selling 80 pens for ₹40. What should be the selling price of 80 pens to earn 10% profit?
Solution:
If SP = ₹40 gives 20% loss, then CP of 80 pens = 40÷(1−0.20)=40÷0.8=₹50  .


To earn 10% on that CP: SP = 50 × 1.10 = ₹55.
Answer: ₹55


Q: Selling at ₹2760 gives a loss equal to the profit obtained by selling at ₹2960. Find the cost price.
Solution:
Let CP = x. Profit at 2960 = 2960 − x. Loss at 2760 = x − 2760.


Given equal: 2960 − x = x − 2760 → 2960 + 2760 = 2x → 5720 = 2x → x = ₹2860.
Answer: ₹2860


Q: Anu sold an article for ₹480 at some profit. Had she sold it for ₹400, there would have been a loss equal to one-third of the initial profit. Find the cost price.
Solution:
Let CP = C. Initial profit P = 480−C . If sold at 400, loss = C − 400.


Given C – 400 = 1/3 P = 1/3 (480−C)


Solve: 3(C−400) =480 – C ⇒ 3C – 1200 = 480 – C ⇒ 4C = 1680 ⇒ C = ₹420
Answer: ₹420


Q. Statement (interpreted): On selling the article at ₹1800 both get a “20%” — Anil calculates profit percentage on SP (i.e. profit = 20% of SP) and Sachin calculates profit percentage on CP (i.e. profit = 20% of CP). Find the difference between their profits (in ₹).


Work:



  • Anil’s profit = 20% of SP = 0.20×1800=₹360

  • Sachin’s profit% on CP = 20% ⇒ SP = 1.2 × CP ⇒ CP = 1800/1.2=₹1500
    Sachin’s profit = 0.20×1500=₹300.


Difference = 360−300=₹60.


Ans: (d) ₹60


Q. Two shopkeepers claim “25% profit” each on the same Selling Price S.



  • Shopkeeper A: 25% on CP (usual) → profit = 25% of CP.

  • Shopkeeper B: 25% on SP → profit = 25% of SP.
    Given difference between their profit amounts = ₹32. Find the Selling Price S.


Work:



  • If SP = S and A’s CP = S/1.25 = 0.8S , A’s profit = S−0.8S=0.2S

  • B’s profit = 0.25S.

  • Difference = 0.25S−0.20S=0.05S=₹32
    So S = 32/0.05 = ₹640.


Ans: ₹640


Q. A man sells two articles for a total of ₹1710.



  • On the first article he has 10% loss.

  • On the second article he has 25% profit.
    Given CP of the first = SP of the second. Find overall profit or loss (and amount).


Work:
Let CP₂ = y. Then SP₂ = 1.25y, Given CP₁ = SP₂ = 1.25y.
SP₁ = CP₁ × 0.9 = 0.9×1.25y=1.125y
Total SP = SP₁ + SP₂ = 1.125y + 1.25y = 2.375y = 1710
So y = 1710/2.375 = 720.
Then CP₁ = 1.25y = 900. CP₂ = 720. Total CP = 900+720=1620,


Total SP = 1710. Total profit = 1710−1620=₹90.


Ans: Profit ₹90 (option (a))


Q. If selling price becomes double, net profit % becomes triple. Find original net profit %.


Work:
Let original SP = S, CP = C. Original profit% = S−C / C × 100
Doubling SP → new profit% = 2S−C / C × 100. Given new profit% = 3 × old profit% ⇒
2S−C / C = 3⋅S−C / C ​.


Solve: 2S−C = 3S−3C → 2C =S
Thus S = 2C → original profit% = S−C / C×100 = C / C×100 = 100%  


Ans: 100%


Q. At what rate of simple interest per annum will a sum of money get doubled in 10 years?


Option : Α. 8.5%  B. 15%  C. 20%  D. 10%


For simple interest, SI = P×R×T/100. To double, SI = P. So, P = P × R × 10 / 100 ⇒ R = 10%


Q: The profit % of Anil and Sachin is same on selling an article at ₹1800 each. But Anil calculates his profit % on Selling Price (SP) and Sachin calculates on Cost Price (CP), both being 20%. Find the difference between their profits.


Options: (a) ₹50  (b) ₹75  (c) ₹65  (d) ₹60


Let’s find Anil’s Cost Price


Anil’s profit % is calculated on SP, i.e.
Profit = 20% of SP
⇒ Profit = 20% of 1800 = (20/100) × 1800 = ₹360


Now,
SP = CP + Profit
1800 = CP + 360
⇒ CP = 1800 − 360 = ₹1440


Sachin’s Cost Price


Sachin’s profit % is on CP, i.e.
Profit = 20% of CP


Let CP = x
Then, SP = x + 0.2x = 1.2x


But SP is the same = ₹1800
⇒ 1.2x = 1800
⇒ x = 1500


Profit = 1800 − 1500 = ₹300


Difference in profit


Difference = 360 − 300 = ₹60


Ans: (d) ₹60


Q: Two shopkeepers claim that they make 25% profit each.One calculates his profit on Cost Price, another on Selling Price.If the difference between their profits is ₹32 and the Selling Price is the same in both cases, find the Selling Price.


Options: (a) ₹960  (b) ₹725  (c) ₹500  (d) ₹640


Let Selling Price = ₹x



  • Shopkeeper 1 (Profit on CP):
    SP = 1.25 × CP
    ⇒ CP₁ = SP / 1.25 = x / 1.25 = 0.8x
    Profit₁ = SP − CP₁ = x − 0.8x = 0.2x

  • Shopkeeper 2 (Profit on SP):
    Profit = 25% of SP = 0.25x
    ⇒ CP₂ = SP − Profit = x − 0.25x = 0.75x


Difference between their profits


Difference = Profit₂ − Profit₁
= 0.25x − 0.2x = 0.05x


Given difference = ₹32
⇒ 0.05x = 32
⇒ x = 32 / 0.05 = ₹640


Ans: (d) ₹640


Q: A person sells two articles for ₹1710. He incurs 10% loss on the first article and gains 25% profit on the second. If the Cost Price of the first article = Selling Price of the second, find the overall profit or loss.


Options: (a) Profit ₹90  (b) Loss ₹90  (c) Profit ₹60  (d) Loss ₹60


Let Cost Price of 1st article = Selling Price of 2nd article = ₹x


Then:



  • For 1st article → 10% loss
    ⇒ SP₁ = 90% of CP₁ = 0.9x

  • For 2nd article → 25% profit
    ⇒ SP₂ = 1.25 × CP₂


We know total SP = 1710
So, SP₁ + SP₂ = 1710
⇒ 0.9x + 1.25CP₂ = 1710


And also given: CP₁ = SP₂ = 1.25CP₂
⇒ CP₁ = 1.25CP₂
⇒ x = 1.25CP₂
⇒ CP₂ = x / 1.25 = 0.8x


Substitute in SP equation:
0.9x + 1.25(0.8x) = 1710
⇒ 0.9x + 1.0x = 1710
⇒ 1.9x = 1710
⇒ x = 900


Now calculate CP and SP


CP₁ = x = 900
CP₂ = 0.8x = 720
Total CP = 900 + 720 = 1620


SP₁ = 0.9x = 810
SP₂ = 1.25 × 720 = 900
Total SP = 1710


Profit/Loss = SP − CP = 1710 − 1620 = +90 (Profit)


Ans: (a) Profit ₹90


Q: If selling price of an article becomes double, the profit % becomes triple. Find the original profit %.


Options: (a) 100%  (b) 133⅓%  (c) 50%  (d) 66⅔%


Let Cost Price = ₹100


Let the original profit% = P%


Then,
Original SP = 100 + P


If SP is doubled, new SP = 2(100 + P)


Now, profit% becomes 3P
So, new profit = 3P% of CP = 3P


New SP = 100 + 3P


Equating both SPs:


2(100 + P) = 100 + 3P
⇒ 200 + 2P = 100 + 3P
⇒ 100 = P


Ans: (a) 100%