A train travels 240 km in 4 hours. If it increases its speed by 20%, how much distance will it cover in 5 hours at the new speed?
Step 1: Calculate the original speed
The train travels 240 km in 4 hours, so we divide distance by time.
Original Speed=4 hours240 km=60 km/h
Step 2: Calculate the new speed after 20% increase
The speed increases by 20%, so we multiply the original speed by 1.20.
New Speed=60×1.20=72 km/h
Step 3: Calculate distance covered in 5 hours at new speed
Distance equals speed multiplied by time.
Distance=72 km/h×5 hours=360 km
The train will cover 360 km in 5 hours at the new speed.
A shopkeeper buys notebooks at ₹40 each and sells them at ₹50 each. If he sells 120 notebooks in a day, what is his total profit?
Step 1: Calculate Total Cost Price
The shopkeeper buys 120 notebooks at ₹40 each.
Total Cost Price=120×40=₹4,800
Step 2: Calculate Total Selling Price
The shopkeeper sells 120 notebooks at ₹50 each.
Total Selling Price=120×50=₹6,000
Step 3: Calculate Total Profit
Profit is the difference between selling price and cost price.
Total Profit=Selling Price−Cost Price=6,000−4,800=₹1,200
The shopkeeper's total profit for selling 120 notebooks in a day is ₹1,200.
A sum of money becomes ₹9,600 after 5 years at a simple interest rate of 8% per annum. What was the principal amount?
Step 1: Identify the Simple Interest Formula
The formula for amount in simple interest is A = P + SI, where SI = PRT/100
A=P+100PRT
Step 2: Substitute Known Values
Given: A = ₹9,600, T = 5 years, R = 8% per annum
9,600=P+100P×8×5
Step 3: Simplify and Solve for Principal
9,600=P+10040P
9,600=P+0.4P
9,600=1.4P
P=1.49,600=1496,000=6,000
The principal amount was ₹6,000.
A person invests ₹5,000 at 6% per annum simple interest. After how many years will the amount become ₹6,500?
Step 1: Identify the given values
Principal (P) = ₹5,000, Rate (R) = 6% per annum, Final Amount (A) = ₹6,500
P=5000,R=6%,A=6500
Step 2: Calculate the Simple Interest
Simple Interest (SI) = Final Amount - Principal
SI=A−P=6500−5000=1500
Step 3: Apply the Simple Interest formula to find Time
Using the formula: SI=100P×R×T
1500=1005000×6×T
1500=10030000×T
1500=300×T
T=3001500=5 years
The amount will become ₹6,500 after 5 years.
A trader buys mangoes at ₹8 per kg and sells them at ₹12 per kg. What is his profit percentage?
Step 1: Identify Cost Price and Selling Price
Cost Price (CP) = ₹8 per kg and Selling Price (SP) = ₹12 per kg
CP=₹8,SP=₹12
Step 2: Calculate Profit
Profit = Selling Price − Cost Price
Profit=₹12−₹8=₹4
Step 3: Calculate Profit Percentage
Profit percentage is calculated as profit divided by cost price, multiplied by 100
Profit%=Cost PriceProfit×100=84×100=21×100=50%
The trader's profit percentage is 50%.
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If an article is purchased for ₹450 and sold at a loss of 8%, what is the selling price?
Step 1: Identify the given information
Cost Price (CP) = ₹450 and Loss = 8%
Given: CP=₹450, Loss=8%
Step 2: Calculate the loss amount
Loss amount = 8% of Cost Price
Loss amount=1008×450=0.08×450=₹36
Step 3: Calculate the selling price
Selling Price = Cost Price − Loss amount
SP=450−36=₹414
The selling price of the article is ₹414.
A retailer buys notebooks at ₹40 each and sells them at ₹50 each. How many notebooks must he sell to make a profit of ₹600?
Step 1: Find profit per notebook
The retailer buys at ₹40 and sells at ₹50, so profit on each notebook is the difference.
Profit per notebook=50−40=₹10
Step 2: Set up equation for total profit
Let the number of notebooks sold be x. The total profit equals profit per notebook multiplied by number of notebooks.
Total Profit=Profit per notebook×Number of notebooks
600=10×x
Step 3: Solve for number of notebooks
Divide both sides by 10 to find x.
x=10600=60
The retailer must sell 60 notebooks to make a profit of ₹600.
Rajesh invested ₹5,000 at a simple interest rate of 8% per annum for 3 years. How much total amount will he receive after 3 years?
Step 1: Use SI formula: SI = (P × R × T) / 100.
Step 2: SI = (5000 × 8 × 3) / 100 = 100120000 = ₹1,200.
Step 3: Total Amount = Principal + SI = 5000 + 1200 = ₹6,200.
So option A is correct.
At what rate of simple interest per annum will ₹8,000 amount to ₹9,600 in 2 years?
Step 1: Find SI = Amount - Principal = 9600 - 8000 = ₹1,600.
Step 2: Use SI = (P × R × T) / 100, so 1600 = (8000 × R × 2) / 100.
Step 3: 1600 = 160R, therefore R = 10%.
So option B is correct.
In how many years will ₹12,000 become ₹15,600 at 6% simple interest per annum?
Step 1: Find SI = 15600 - 12000 = ₹3,600.
Step 2: Use SI = (P × R × T) / 100, so 3600 = (12000 × 6 × T) / 100.
Step 3: 3600 = 720T, therefore T = 5 years.
So option B is correct.
Priya lent ₹10,000 to her friend at 5% simple interest per annum. After 2.5 years, how much interest will she receive?
Step 1: Use SI formula: SI = (P × R × T) / 100.
Step 2: SI = (10000 × 5 × 2.5) / 100 = 100125000 = ₹1,250.
Step 3: The interest earned is ₹1,250.
So option B is correct.
What will be the compound interest on ₹5,000 at 8% per annum for 2 years, compounded annually?
Step 1: Use formula A = P(1 + r/100)^n.
Step 2: A = 5000(1 + 1008)^2 = 5000(1.08)^2 = 5000 × 1.1664 = 5832.
Step 3: CI = A - P = 5832 - 5000 = ₹832.
So option A is correct.
At what rate of interest per annum will ₹8,000 amount to ₹9,261 in 3 years, compounded annually?
Step 1: Use A = P(1 + r/100)^n.
Step 2: 9261 = 8000(1 + r/100)^3.
Step 3: (1 + r/100)^3 = 80009261 = 1.157625.
Step 4: Taking cube root, 1 + r/100 = 1.05, so r = 5%.
So option B is correct.
In how many years will ₹10,000 become ₹13,310 at 10% per annum compound interest?
Step 1: Use A = P(1 + r/100)^n formula.
Step 2: 13310 = 10000(1 + 10010)^n = 10000(1.1)^n.
Step 3: 1.331 = (1.1)^n.
Step 4: Taking log or testing: (1.1)^3 = 1.331.
Therefore n = 3 years.
So option C is correct.
A shopkeeper buys a shirt for ₹400 and sells it for ₹520. What is his profit percentage?
Step 1: Profit = Selling Price - Cost Price = 520 - 400 = ₹120.
Step 2: Profit% = (Profit/CP) × 100 = (400120) × 100 = 30%.
So option B is correct.
A merchant sells a watch at a loss of 12%. If the cost price is ₹1,500, what is the selling price?
Step 1: Loss = 12% of CP = 0.12 × 1,500 = ₹180.
Step 2: SP = CP - Loss = 1,500 - 180 = ₹1,320.
So option B is correct.
If an article is sold at ₹810 with a profit of 35%, what was its cost price?
Step 1: Let CP = x. SP = CP + Profit = x + 0.35x = 1.35x.
Step 2: 1.35x = 810, so x = 1810.35 = ₹600.
So option A is correct.
A trader buys 50 kg of sugar at ₹40 per kg and sells it at ₹48 per kg. What is the total profit?
Step 1: Total Cost Price = 50 × 40 = ₹2,000.
Step 2: Total Selling Price = 50 × 48 = ₹2,400.
Step 3: Total Profit = 2,400 - 2,000 = ₹400.
So option C is correct.
A merchant buys cloth at ₹450 per meter and sells it at ₹540 per meter. What is the profit percentage?
Step 1: Cost Price (CP) = ₹450 per meter.
Step 2: Selling Price (SP) = ₹540 per meter.
Step 3: Profit = SP - CP = 540 - 450 = ₹90.
Step 4: Profit% = (Profit/CP) × 100 = (45090) × 100 = 20%.
So option B is correct.
If an article costs ₹640 and is sold at a loss of 8%, what is the selling price?
Step 1: Cost Price = ₹640.
Step 2: Loss = 8% of 640 = 0.08 × 640 = ₹51.20.
Step 3: Selling Price = CP - Loss = 640 - 51.20 = ₹588.80.
So option B is correct.
