Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A retailer buys a radio for Rs. 215. His overhead expenses are Rs. 25. If he sells the radio for Rs. 300, his profit will be
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Step-by-Step Explanation & Concept Rationale
Total CP=215+25=240.
Profit = 300−240=60.
% = (60/240)×100=25%.
Profit = 300−240=60.
% = (60/240)×100=25%.
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Watch bought for Rs. 400, sold at gain of 10%. Selling price?
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Step-by-Step Explanation & Concept Rationale
SP=400×1.10=440.
Q. 3
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
If a washing machine is sold for Rs. 660 at a loss of 12%. Its cost price should be
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Step-by-Step Explanation & Concept Rationale
CP=660/(1−0.12)=660/0.88=750.
Q. 4
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
By selling 200 oranges, a man gains the selling price of 40 oranges. His gain percent is
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Step-by-Step Explanation & Concept Rationale
Set up the variables:
Let the selling price (SP) of 1 orange be Rs. 1.
Then, the total selling price of 200 oranges = Rs. 200
The gain equals the selling price of 40 oranges = Rs. 40
Calculate the total Cost Price (CP):
Using the profit formula (\(CP = SP - \text{Gain}\)):
\(\text{Total CP}=200-40=\text{Rs. }\mathbf{160}\)
Calculate the Gain Percentage:
Profit percentage is always calculated relative to the Cost Price:
\(\text{Gain Percentage}=\left(\frac{\text{Gain}}{\text{Total CP}}\right)\times 100\%\)
\(\text{Gain Percentage}=\left(\frac{40}{160}\right)\times 100\%=\frac{1}{4}\times 100\%=\mathbf{25\%}\)
Let the selling price (SP) of 1 orange be Rs. 1.
Then, the total selling price of 200 oranges = Rs. 200
The gain equals the selling price of 40 oranges = Rs. 40
Calculate the total Cost Price (CP):
Using the profit formula (\(CP = SP - \text{Gain}\)):
\(\text{Total CP}=200-40=\text{Rs. }\mathbf{160}\)
Calculate the Gain Percentage:
Profit percentage is always calculated relative to the Cost Price:
\(\text{Gain Percentage}=\left(\frac{\text{Gain}}{\text{Total CP}}\right)\times 100\%\)
\(\text{Gain Percentage}=\left(\frac{40}{160}\right)\times 100\%=\frac{1}{4}\times 100\%=\mathbf{25\%}\)
Q. 5
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A man sells two watches at Rs. 99 each. On one he gains 10% and on the other he losses 10%. His gain of loss per cent is
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Step-by-Step Explanation & Concept Rationale
The formula for the total loss percentage is:
\(\text{Loss Percentage}=\left(\frac{x}{10}\right)^{2}\%\)
Given \(x = 10\):
\(\text{Loss Percentage}=\left(\frac{10}{10}\right)^{2}\%=(1)^{2}\%=\mathbf{1\%}\)
\(\text{Loss Percentage}=\left(\frac{x}{10}\right)^{2}\%\)
Given \(x = 10\):
\(\text{Loss Percentage}=\left(\frac{10}{10}\right)^{2}\%=(1)^{2}\%=\mathbf{1\%}\)
Q. 6
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
By selling oranges at 32 for a rupee, a man lost 40%. How many for a rupee must he sell so as to gain 20%?
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Step-by-Step Explanation & Concept Rationale
Find the price factors:
Case 1 (40% loss): Selling price is \(100\% - 40\% = 60\%\) of Cost Price.
Case 2 (20% gain): Desired selling price is \(100\% + 20\% = 120\%\) of Cost Price.
Set up the inverse proportion:
\(\text{Initial Quantity}\times \text{Initial Price Factor}=\text{New Quantity}\times \text{New Price Factor}\)
\(32\times 60\%=\text{New Quantity}\times 120\%\)
Solve for the New Quantity:
\(\text{New Quantity}=\frac{32\times 60}{120}=\frac{32}{2}=\mathbf{16}\)
Case 1 (40% loss): Selling price is \(100\% - 40\% = 60\%\) of Cost Price.
Case 2 (20% gain): Desired selling price is \(100\% + 20\% = 120\%\) of Cost Price.
Set up the inverse proportion:
\(\text{Initial Quantity}\times \text{Initial Price Factor}=\text{New Quantity}\times \text{New Price Factor}\)
\(32\times 60\%=\text{New Quantity}\times 120\%\)
Solve for the New Quantity:
\(\text{New Quantity}=\frac{32\times 60}{120}=\frac{32}{2}=\mathbf{16}\)
Q. 7
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Adealer for horses sold two horses for Rs. 500 each. On one of them he lost 10% and on the other he gained 10%. The percentage of his loss or gain is
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Step-by-Step Explanation & Concept Rationale
Total CP = 1000.
Total SP = 450+550=1000.
Break even.
Total SP = 450+550=1000.
Break even.
Q. 8
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A shopkeeper gains 20% after allowing 10% discount on the list price. What will be his gain per cent if he allows 20% discount on the list price?
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Step-by-Step Explanation & Concept Rationale
CP=75,MP=100.
With 20% disc,
SP=80.
Gain % = (5/75)×100=6.66%.
With 20% disc,
SP=80.
Gain % = (5/75)×100=6.66%.
Q. 9
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
By selling goods at Rs. 31, a merchant loses 7% on his outlay. If he sells the same goods at Rs. 35, the percentage of profit or loss is
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Step-by-Step Explanation & Concept Rationale
CP=31/0.93=33.33.
Sells at 35
⟹ profit = Rs. 1.66.
Profit% = (1.66/33.33)×100=5%.
Sells at 35
⟹ profit = Rs. 1.66.
Profit% = (1.66/33.33)×100=5%.
Q. 10
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A sells an article to B at a gain of 20%; B sells to C at a gain of 25% and C sells to D at a gain of 40%, if it costs A Rs. 50; what does D pay for it?
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Step-by-Step Explanation & Concept Rationale
Final Price = 50×1.2×1.25×1.4=105.
Q. 11
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A bicycle is sold at 20% profit, if it had been sold at 20% loss, the selling price would have been Rs. 100 less. The cost of the bicycle is
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Step-by-Step Explanation & Concept Rationale
Case 1 (20% Profit):
The selling price is \(100\% + 20\% = \mathbf{120\% \text{ of CP}}\)
Case 2 (20% Loss):
The selling price is \(100\% - 20\% = \mathbf{80\% \text{ of CP}}\)
Difference is 40% of CP.
0.4CP=100
⟹CP=250.
The selling price is \(100\% + 20\% = \mathbf{120\% \text{ of CP}}\)
Case 2 (20% Loss):
The selling price is \(100\% - 20\% = \mathbf{80\% \text{ of CP}}\)
Difference is 40% of CP.
0.4CP=100
⟹CP=250.
Q. 12
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
By selling a horse for Rs. 75 a man would loss 4%. For what amount should he sell it to gain 40?
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Step-by-Step Explanation & Concept Rationale
CP=75/0.96=78.125.
New SP=78.125×1.4≈110.
New SP=78.125×1.4≈110.
Q. 13
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A man sold article at a gain of 16%. If he had sold it for Rs. 16 more he would have gained 20%. The cost price of the articie is
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Step-by-Step Explanation & Concept Rationale
Difference 4% = Rs. 16.
CP=16/0.04=400.
CP=16/0.04=400.
Q. 14
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A brought a radio and spent Rs. 110 on its repairs. He then sold it to B at 20% profit, B sold to C at a loss of 10%. C sold it for Rs. 1188 at a profit of 10%. A bought the radio for
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Step-by-Step Explanation & Concept Rationale
Working backward:
1188/1.1/0.9/1.2=1000.
Purchase Price = 1000−110=890.
1188/1.1/0.9/1.2=1000.
Purchase Price = 1000−110=890.
Q. 15
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A manufacturer sells goods to an agent at a profit of 20%. The agents wholesale price to a shopkeeper is at a profit of 10% and the shopkeeper retails his goods at a profit of 12 1/2%. The manufacturing cost of goods bought in the shop for Rs. 14.85 is
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Step-by-Step Explanation & Concept Rationale
Cost×1.2×1.1×1.125=14.85
⟹Cost=14.85/1.485=10.
⟹Cost=14.85/1.485=10.
Q. 16
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A man sold his watch at a loss of 5%. Had he sold it for Rs. 56.25 more he would have gained 10%. The cost price of the watch is
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Step-by-Step Explanation & Concept Rationale
Difference 15% = 56.25.
CP=56.25/0.15=375.
CP=56.25/0.15=375.
Q. 17
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A trademan's prices are 25% above cost price, but he allows his customer 12% commission on the amounts of their bills. He makes a profit of
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Step-by-Step Explanation & Concept Rationale
CP=100,MP=125,
SP=125×0.88=110.
Profit = 10%.
SP=125×0.88=110.
Profit = 10%.
Q. 18
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A horse was sold at a loss of 10 per cent, if it was sold for Rs. 70 more, there would have been a gain of 40%. The horse was bought in
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Step-by-Step Explanation & Concept Rationale
Difference 50% = 70.
CP=70/0.5=140.
CP=70/0.5=140.
Q. 19
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A dealer allows 10% discount on the list price of certain articles and yet makes a profit of 25% on each article. The cost price of an article whose listed price is Rs. 50 will be
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Step-by-Step Explanation & Concept Rationale
SP=50×0.9=45.
CP=45/1.25=36.
CP=45/1.25=36.
Q. 20
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A tradesman marksan article with a price which would give him a profit of 20% on the cost price.If the customer pays cash, however the tradesman makes a deduction of 5% from the market price, find the actual profit recieved from the sale of an article for which the tradesman is paid Rs. 28.50
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Step-by-Step Explanation & Concept Rationale
Find Selling Price (SP) relative to Cost Price (CP):
Marked Price = 120% of CP
SP after 5% discount = \(120\% - (5\% \text{ of } 120) = \mathbf{114\% \text{ of CP}}\)
Calculate CP:\(114\% \text{ of CP} = 28.50\)
\(\text{CP} = \frac{28.50}{1.14} = \mathbf{\text{Rs. } 25}\)
Calculate Profit:
\(\text{Profit} = 28.50 - 25 = \mathbf{\text{Rs. } 3.50}\)
Marked Price = 120% of CP
SP after 5% discount = \(120\% - (5\% \text{ of } 120) = \mathbf{114\% \text{ of CP}}\)
Calculate CP:\(114\% \text{ of CP} = 28.50\)
\(\text{CP} = \frac{28.50}{1.14} = \mathbf{\text{Rs. } 25}\)
Calculate Profit:
\(\text{Profit} = 28.50 - 25 = \mathbf{\text{Rs. } 3.50}\)
Q. 21
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A tradesman marks his good at 25% above CP. if he allows his customers 10% discount, how much % profit does he make?
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Step-by-Step Explanation & Concept Rationale
SP=1.25×0.9=1.125
⟹ profit of 12.5%.
⟹ profit of 12.5%.
Q. 22
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A man sold his watch at a loss of 5%. Had he sold it for Rs. 56.25 more he would have gain 10%. Find the cost price of watch
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Step-by-Step Explanation & Concept Rationale
The 15% difference is equal to Rs. 56.25:
\(15\%\text{ of CP}=56.25\)
\(\text{CP}=\frac{56.25}{0.15}=\mathbf{375}\)
\(15\%\text{ of CP}=56.25\)
\(\text{CP}=\frac{56.25}{0.15}=\mathbf{375}\)
Q. 23
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A person purchased a horse and a carriage for Rs. 1800. He sold the horse at a profit of 20% and the carriage at a profit of 30%. His total profit was 25 5/6 %
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Step-by-Step Explanation & Concept Rationale
Find the profit ratios:
Horse profit: 20%
Carriage profit: 30%
Total mean profit: \(25 \frac{5}{6}\% = \mathbf{\frac{155}{6}\%}\)
Set up the alligation cross (multiply by 6 to remove fractions):
Horse: \(20 \times 6 = \mathbf{120}\)
Carriage: \(30 \times 6 = \mathbf{180}\)
Mean: \(\frac{155}{6} \times 6 = \mathbf{155}\)
Calculate the ratio of Cost Prices (Horse : Carriage):
(Carriage side): \(180 - 155 = \mathbf{25}\)
(Horse side): \(155 - 120 = \mathbf{35}\)
Ratio = \(25 : 35 = \mathbf{5 : 7}\)
Split the total cost (Rs. 1800):
Total parts = \(5 + 7 = 12\) parts
\(12 \text{ parts} = 1800 \implies 1 \text{ part} = 150\)
Cost of Horse = \(5 \times 150 = \mathbf{750}\)
Horse profit: 20%
Carriage profit: 30%
Total mean profit: \(25 \frac{5}{6}\% = \mathbf{\frac{155}{6}\%}\)
Set up the alligation cross (multiply by 6 to remove fractions):
Horse: \(20 \times 6 = \mathbf{120}\)
Carriage: \(30 \times 6 = \mathbf{180}\)
Mean: \(\frac{155}{6} \times 6 = \mathbf{155}\)
Calculate the ratio of Cost Prices (Horse : Carriage):
(Carriage side): \(180 - 155 = \mathbf{25}\)
(Horse side): \(155 - 120 = \mathbf{35}\)
Ratio = \(25 : 35 = \mathbf{5 : 7}\)
Split the total cost (Rs. 1800):
Total parts = \(5 + 7 = 12\) parts
\(12 \text{ parts} = 1800 \implies 1 \text{ part} = 150\)
Cost of Horse = \(5 \times 150 = \mathbf{750}\)
Q. 24
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A sells his goods 10% cheaper than B, and 10% dearer than C. How much would a customer of B save by purchasing Rs. 100 worth of goods from C?
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Step-by-Step Explanation & Concept Rationale
A=0.9B,A=1.1C
⟹0.9B=1.1C
⟹C=9/11B≈81.8%.
Error is $21 \frac{4}{9}$%.
⟹0.9B=1.1C
⟹C=9/11B≈81.8%.
Error is $21 \frac{4}{9}$%.
Q. 25
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A tradesman marks his goods 25% above cost price. If he allows his customer 10% discount, how much% profit does he make?
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Step-by-Step Explanation & Concept Rationale
Result is 12.5%.
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