Find Profit & Loss 5
Q. The cost price (CP) of 15 items is equal to the selling price (SP) of 10 items. Find the profit or loss %.
Rule : General Profit/Loss Formula
Profit = SP - CP
Loss = CP - SP
Profit % = Profit/CP×100
Loss % = Loss/CP×100
Soln
X = 15, Y = 10
Profit % = 15−10/10 ā× 100 = 50%
Ans: 50% Profit
Math Formula : Click Here
Q. Due to a 12% decrease in the price of rice, a person can buy 1 quintal more rice with 6000 taka than before. What is the current price of 1 quintal of rice ?
Options: (a) 750 (b) 75 (c) 700 (d) 720
Soln:
When the price decreases by 12%, the new price becomes:
New price = (100 – 12) = 88 (If the old price was 100)
So, the ratio of old price to new price = 100 : 88
If rice was bought for 6000 taka at present rate, the amount of money equivalent to the old price is: 100/88 × 6000 = Rs 5280
So, the extra money gained due to the price decrease: 6000 - 5280 = Rs720
This extra Rs720 buys 1 quintal more,
so the current price of 1 quintal rice = Rs 720.
Ans: (d) 720
Short Trick : Extra quantity gained = Money × % decrease → 6000 × 12% = 720
Price decreased by 12%, so current price = 88% of old price.
Extra amount saved = 6000×12/100 = 720
This extra Rs 720 = price of 1 quintal (because you can buy 1 quintal more).
Current Price of 1 Quintal Rice = Rs720
Math Formula : Click Here
Q. The speed of the launch is 18 km/h and the speed of the stream is 6 km/h. How much time will it take to go 48 km downstream and return 48 km upstream ?
Options: (a) 10 hours (b) 6 hours (c) 5 hours (d) 8 hours
Ans: (b) 6 hours
Soln:
Downstream Speed (with current): 18 + 6 = 24 km/h
Time to cover 48 km downstream: 48 ÷ 24 = 2 hours
Upstream Speed (against current): 18 - 6=12 km/h
Time to cover 48 km upstream: 48 ÷ 12 = 4 hours
Total Time: 2 + 4 = 6 hours
Ans: 6 hours
Short Trick
Downstream time = Distance ÷ (Boat speed + Stream speed)
48 ÷ (18 + 6) = 48 ÷ 24 = 2 hours
Upstream time = Distance ÷ (Boat speed – Stream speed)
48 ÷ (18 - 6) = 48 ÷ 12 = 4 hours
Total Time : 2+4 = 6 hours
Short Trick : Total Time = D / (B + S) + D / (B - Sā)
Put values: = 48/24 + 48/12
= 2 + 4 = 6 hours
Math Formula : Click Here
Q. Selling 12 lemons for ā¹1 causes 4% loss. To get 44% profit, how many lemons should be sold for ā¹1?
Soln
Find the Cost Price
At 4% loss, Selling Price (SP) = 96 , Cost Price (CP) = 100
So, When SP = 96 → CP = 100
Cost price of 12 lemons = Rs100, So, cost price of 1 lemon:
CP of 1 lemon = 100/12
Find Required Selling Price for 44% Profit
44% profit means: New SP = 100+44 = 144
So CP = 100 corresponds to SP = 144.
Lemons to Sell for Rs1
If SP of Rs100 corresponds to Rs 144, then SP of Rs 1 corresponds to:
Lemons per Rs = 12×144/100
Simplify using the solution steps:
=25×144/24×100
=2×12/3
=8 lemons
Ans: 8 lemons
Soln (Short):
- At 4% loss → SP = 96, CP = 100
- For 44% profit → SP = 144
- Number of lemons for ā¹1: 12 × 100 + 44/100 + (−4) = 8 lemons
Ans: 8 lemons
Q. A man sells an item at 15% profit and at 17% loss. The difference between the two selling prices is ā¹96. If he sells the item at 10% profit, what will be the selling price ?
Soln.
Find % difference between SPs : 15% profit and 17% loss →15+17 = 32%
Convert percentage into money
Given:
32% = ā¹96
So,
1% = 96/32 = ā¹3
SP at 10% profit : SP = 110% of CP
110% = 110×3 = ā¹330
Answer: ā¹330
Math Formula : Click Here
Q: A mobile phone is sold for ā¹59,620 at a profit of 8.4%. What is the cost price (CP) ?
Trick:- Just use: CP = SP×100/100+Profit%
1st Selling price is 108.4% of CP (Because CP = 100%)
2nd Compare % with money : 108.4%=ā¹59,620
3rd : Convert to easy numbers
108.4% = 1084 (remove decimal)
100% = 1000
4th : CP = (1000 ÷ 1084) × 59,620
This approx becomes: CP=ā¹55,000
Ans: ā¹55,000
Q. If an item is sold for ā¹355, there is a 29% loss. At what price should it be sold to gain 31% profit ?
Soln,
Loss 29% → Selling Price = 71% of CP
(Because 100 – 29 = 71)
Profit 31% → Required SP = 131% of CP
(Because 100 + 31 = 131)
So we compare the % values: 71% = ā¹355
Find CP:
CP = 355/71×100 = 500
Find new SP for 31% profit:
SP = 131% of CP = 131/100×500 = ā¹655
Ans: ā¹655
Q. The difference between the selling price (SP) and cost price (CP) of an item is ā¹1,800. If there is a 20% profit, find the cost price (CP) of the item.
Trick Soln
Represent in “units”
- Profit = 20% → SP = 120% of CP
- Let CP = 100 units → SP = 120 units
- Difference = 120 – 100 = 20 units
Find the value of 1 unit
20 units = ā¹1,800ā āā¹ā ā1 unit=1800÷20=ā¹90
Find CP :
CP = 100 units×ā¹90 = ā¹9,000
Ans: CP = ā¹9,000
Math Formula : Click Here
Q. The cost price (CP) of 44 items is equal to the selling price (SP) of X items. If there is a 10% profit, find the value of X.
CP of 44 items = SP of X items. Profit = 10%. Find X.
Soln
Trick: Profit 10% → SP
SP = CP+10% of CP=CP+0.1 CP=1.1 CP=11/10 CP
Formula: X = CP items / SP per item as fraction of CP = 44 divide 11/10 = 44×10/11 = 40
Ans: X = 40