Find Profit & Cost Price 4

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Q. A gold ornament weighs 32 grams. The ratio of gold to copper is 3 : 1. How much gold must be added to make the ratio 4 : 1?

Solⁿ:

Find gold and copper in 32 g

Total parts = 3 + 1 = 4
Gold = 3/4×32 = 24g
Copper = 1/4×32=8 g

Let the added gold = x grams

New gold amount = 24+x
Copper remains = 8 g

Given new ratio = 4 : 1

So,

24 + x/8 = 4

Solve

24 + x = 32

X = 32−24 = 8

Ans: 8 grams of gold must be added.

Math Formula : Link 1 / Link 2

Q. The total amount (Principal + Interest) after 3 years is ₹5500. The ratio of Principal : Interest = 8 : 3. Find the Principal and the Rate of Interest.

Solⁿ,

Total ratio = 8 + 3 = 11

11 parts = 5500
So, 1 part = 5500 ÷ 11 = 500

Principal = 8 parts

P = 8 × 500 = ₹4000

Interest = 3 parts

I = 3 × 500 = ₹1500

Rate

Use simple interest formula: r = (I × 100) ÷ (P × n)

           r = (1500 × 100) ÷ (4000 × 3)
           r = 12.5%

Ans: Principal = ₹4000 & Rate = 12.5%

Q. A seller gives 5% discount on the marked price but still makes 25% profit on the cost price. If the cost price of the book is Rs 380, what was the marked price?

Solⁿ

Find Selling Price (SP) from Cost Price (CP)

CP = Rs 380
Profit = 25%

Selling Price
= CP + 25% of CP
= 380 + (25% of 380)
= 380 + 95
= Rs 475

So, the book is sold for Rs 475  after giving the discount.

Remove the 5% Discount to get Marked Price

If marked price = Rs 100
Then after 5% discount, selling price = Rs 95

So,
Selling price 95 → Marked price 100
Selling price 475 → Marked price = ?

Marked Price = (475 × 100) / 95 = Rs 500

Ans: Marked Price = Rs 500

Shortcut Memory Trick

MP = SP × 100 / (100 – Discount%)

Just plug-in: MP = 475 × 100 / 95 = Rs 500

Q. A book costs Rs 100. To increase sales, the price is reduced by 10%. After 3 months, an additional 5% discount is given on the new price. For how much is the book finally sold ?

Solⁿ

• Original price = Rs 100


• First discount = 10% of 100 = Rs 10


• New price after first discount = 100 - 10 = Rs 90


• Second discount = 5% of 90 = 4.5 taka


• Price after second discount = 90 – 4.5 = Rs 85.5


• Final Selling Price = Rs 85.5

Q) MP = 150% of CP. Discount 30%. Profit% ?

Solⁿ

MP = 150% of CP
Discount = 30%

Let CP = 100
→ MP = 150
→ SP = 150 × 70% = 105

Profit = 105 − 100 = 5
Profit% = 5%

Ans: 5% Profit

Math Formula : Link 1 / Link 2

Q. If 15 pens are bought for ₹75 and sold for ₹90, find the percentage of profit.

Solⁿ.
Cost Price (C.P.) = ₹75
Selling Price (S.P.) = ₹90

Profit = S.P. – C.P.
= 90 – 75
= ₹15

Percentage of Profit = (Profit ÷ C.P.) × 100
= (15 ÷ 75) × 100
= 20%

Profit = 20%

Q. A bag is sold for ₹69 at an 8% loss. If it is sold for ₹78, find the percentage of profit or loss.

Soⁿ:

At 8% loss,
Selling Price (S.P.) = ₹92 corresponds to Cost Price (C.P.) = ₹100

Now, when S.P. = ₹69,

C.P.= 100×69/92 = 75

So, C.P. = ₹75

If sold at ₹78,
Profit = S.P. – C.P. = 78 – 75 = ₹3

Percentage of Profit =3/75×100=4%  

Ans: 4% profit

Q. Successive discount 10% and 20% then extra 5% for cash — total discount ?

Trick: multiply complements: 0.90 × 0.80 × 0.95 = 0.684
Total discount = 1− 0.684 = 0.316 = 31.6%

Ans: (c) 31.6%

Given: Discounts = 10%, 20%, 5%

Convert discounts to complements

• 10% → 0.90


• 20% → 0.80


• 5% → 0.95

Multiply complements

0.90 × 0.80 × 0.95 = 0.684

Convert to total discount

Total discount = 1− 0.684 = 0.316 = 31.6%

Ans: 31.6%

Q. Buy 15 get 1 free and additional 4% discount — equivalent single discount ?

Shortcut: Convert free items into % discount, multiply with other discounts

Free fraction
Buy 15 get 1 free → total items = 16 → fraction free = 1/16 = 0.0625 = 6.25%

Combine with 4% discount
Effective multiplier = (1 − 0.0625) × (1 − 0.04) = 0.9375 × 0.96 = 0.90

Total discount

1−0.90 = 0.10 = 10%

Ans: 10%

Q) MP = 150% of CP. Discount 30%. Profit% ?

Shortcut: SP % of CP = MP% × (1 − discount%), then subtract 100.

Tricks : Let CP = 100 → MP = 150 → SP = 150×0.70 = 105. Profit = 105 − 100 = 5 → 5% profit.

Ans: 5%

Assume CP = 100

• MP = 150% of CP → 150

Apply discount

     SP = 150 × (1−0.30) = 150 × 0.7 = 105

Step 3: Calculate profit%

Profit = SP – CP = 105 – 100 = 5 ⇒5%

Ans: 5% profit

Q) MP = 160% of CP. Discount 20%. Profit% ?

Shortcut: Same as above, easy mental math.

SP as % of CP = 160% × 0.8 = 128% . Profit% = 128−100 = 28% .

Ans: 28%

SP as % of CP = 160 × (1 − 0.20) = 160 × 0.8 = 128

Profit% = SP % − 100 = 128 − 100 = 28%

Ans: 28%

Q) Marked 20% above CP, discount 15% — gain or loss%?

Shortcut: Always find SP as % of CP, compare to 100.

CP = 100 → MP = 120 → SP = 120×0.85 = 102 → profit = 2 → 2% gain..

Ans: 2% gain

CP = 100 → MP = 100 + 20% = 120

Apply 15% discount : SP = 120×0.85 = 102

Profit% = SP − CP = 102 − 100 = 2%

Ans: 2% gain

Q. The cost price of 25 books is equal to the selling price of 20 books.Find the Profit Percentage.

A. 20%  B. 22%  C. 24%  D. 25%

Soln,

25 books C.P. = 20 books S.P.
→ 25CP=20SP25CP = 20SP25CP=20SP
→ SP/CP=25/20=1.25SP/CP = 25/20 = 1.25SP/CP=25/20=1.25

Profit % = (1.25 − 1) × 100 = 25%

Q. If the cost price of 28 items is equal to the selling price of 21 items, find the profit percentage.

A. 12%  B. 100/3%  C. 20%  D. 25%

Soln

28 items C.P. = 21 items S.P.
→ 28CP=21SP28CP = 21SP28CP=21SP
→ SP/CP=28/21=4/3=1.333SP/CP = 28/21 = 4/3 = 1.333SP/CP=28/21=4/3=1.333

Profit % = (1.333 − 1) × 100 = 33.33% (100/3%)

Answer: (B) 100/3%

Q.  If the selling price of 16 items is equal to the cost price of 20 items, then we will get —

A. 25% profit  B. 20% profit  C. 20% loss  D. 4% loss

Soln

16 items S.P. = 20 items C.P.
→ 16SP=20CP16SP = 20CP16SP=20CP
→ SP/CP=20/16=1.25SP/CP = 20/16 = 1.25SP/CP=20/16=1.25

Profit % = (1.25 − 1) × 100 = 25%

Answer: (A) 25% Profit

Q. If the cost price of 20 oranges is equal to the selling price of 16 oranges, then what will be the percentage of profit ?

A. 30%  B. 20%  C. 25%  D. 16%

Given:

Cost price of 20 oranges = selling price of 16 oranges
→ 20CP=16SP

SP/CP=20/16=1.25

Profit %:

(1.25−1)×100=25%

Answer: (C) 25% Profit

Math Formula : Link 1 / Link 2

General Tip for Profit/Discount Questions

• Convert all percentages into multipliers: 10% → 0.90, 20% → 0.80.


• Always think SP as % of CP to directly get profit/loss %.


• Combine successive discounts by multiplying complements.


• Convert free items in “Buy m Get n free” into fraction of total items.