Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Spending Rs 10.00 on 50p and 20p stamps; greatest number of 50p stamps?
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Step-by-Step Explanation & Concept Rationale
18×50p=900p. Remaining 100p allows 5×20p stamps. Total is 1000p (Rs 10).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
How many three-figure can be formed from the digits 2, 6, 3, 5, 1?
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Step-by-Step Explanation & Concept Rationale
Identify the variables:
Total number of available digits (\(n\)) = 5 (the digits are 2, 6, 3, 5, 1).
Number of digits to choose at one time (\(r\)) = 3.
Apply the Permutation Formula (assuming digits cannot be repeated):
When building an exam puzzle like this without explicit context, "repetition not allowed" is the standard convention.
\({}^{n}P_{r}=\frac{n!}{(n-r)!}\)
\({}^{5}P_{3}=\frac{5!}{(5-3)!}=\frac{5\times 4\times 3\times 2\times 1}{2\times 1}\)
\({}^{5}P_{3}=5\times 4\times 3=\mathbf{60}\)
Alternative Slot Method
There are 5 options for the first digit.
After picking the first digit, 4 options remain for the second digit.
After picking the second digit, 3 options remain for the third digit.
\(\text{Total Permutations}=5\times 4\times 3=\mathbf{60}\)
Total number of available digits (\(n\)) = 5 (the digits are 2, 6, 3, 5, 1).
Number of digits to choose at one time (\(r\)) = 3.
Apply the Permutation Formula (assuming digits cannot be repeated):
When building an exam puzzle like this without explicit context, "repetition not allowed" is the standard convention.
\({}^{n}P_{r}=\frac{n!}{(n-r)!}\)
\({}^{5}P_{3}=\frac{5!}{(5-3)!}=\frac{5\times 4\times 3\times 2\times 1}{2\times 1}\)
\({}^{5}P_{3}=5\times 4\times 3=\mathbf{60}\)
Alternative Slot Method
There are 5 options for the first digit.
After picking the first digit, 4 options remain for the second digit.
After picking the second digit, 3 options remain for the third digit.
\(\text{Total Permutations}=5\times 4\times 3=\mathbf{60}\)
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
A-10 litre mixture of milk and water cóntains 30 percent water. Two litres of this mixture is taken away. How many litres of water should now be added so that the amount of milk in the mixture is double that of water.
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Step-by-Step Explanation & Concept Rationale
Remaining mixture: 10 litres - 2 litres = 8 litres.
Milk in remaining mixture: 70% of 8 litres = 5.6 litres.
Water in remaining mixture: 30% of 8 litres = 2.4 litres.
Target ratio: Milk must be double the water.
Required water volume: 5.6 litres / 2 = 2.8 litres.
Water to add: 2.8 litres - 2.4 litres = 0.4 litres.
Milk in remaining mixture: 70% of 8 litres = 5.6 litres.
Water in remaining mixture: 30% of 8 litres = 2.4 litres.
Target ratio: Milk must be double the water.
Required water volume: 5.6 litres / 2 = 2.8 litres.
Water to add: 2.8 litres - 2.4 litres = 0.4 litres.
Q. 4
Intelligence Tests
Difficulty: Hard
(1 Mark)
Ali is 20 years younger than 3/5 of his actual age. What is the present age of Ali?
Correct Answer / Solution Key:
50 years
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Step-by-Step Explanation & Concept Rationale
Derived from the equation x−3/5x=20⟹2/5x=20⟹x=50.
Q. 5
Intelligence Tests
Difficulty: Hard
(1 Mark)
Javed increases his speed half as much again and Usman increases his twice as much again. Initial speed 8. Difference?
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Step-by-Step Explanation & Concept Rationale
Javed: 8+4=12. Usman: 8+16=24. Difference: 24−12=12.
Q. 6
Intelligence Tests
Difficulty: Hard
(1 Mark)
In a partitioned room there are cats and fowls. They have 15 heads and 50 feet. How many cats?
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Step-by-Step Explanation & Concept Rationale
C+F=15 and 4C+2F=50. Solving for C yields 10 cats and 5 fowls.
Q. 7
Intelligence Tests
Difficulty: Hard
(1 Mark)
A is 5 years younger than B who is 3 times old as C. C was 10, 4 years ago. A's age?
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Step-by-Step Explanation & Concept Rationale
C is 14; B is 42; A is 42−5=37. [Note: key refers to present age].
Q. 8
Intelligence Tests
Difficulty: Hard
(1 Mark)
Find a number which when divided by 4 exceeds 80 by as much as it short of 160 now.
Correct Answer / Solution Key:
120
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Step-by-Step Explanation & Concept Rationale
Derived from the equation x/4−80=160−x/4⟹2x/4=240⟹x/4=120.
Q. 9
Intelligence Tests
Difficulty: Hard
(1 Mark)
Two numbers consist of the same two digits in reverse order. If the difference is 54, what are the numbers?
Correct Answer / Solution Key:
(28, 82)
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Step-by-Step Explanation & Concept Rationale
82−28=54; these two digits (2, 8) in reverse satisfy the problem's criteria.
Q. 10
Intelligence Tests
Difficulty: Hard
(1 Mark)
My age is 3/4th of my brother’s age and the difference is 6 years. My brother’s age?
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Step-by-Step Explanation & Concept Rationale
B−3/4B=6⟹1/4B=6⟹B=24.
Q. 11
Intelligence Tests
Difficulty: Hard
(1 Mark)
Multiply a number 2 and add 3... added 3 first and multiplied by 2... got 20. Correct answer?
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Step-by-Step Explanation & Concept Rationale
Second student: 2(x+3)=20⟹x=7. First student: 2(7)+3=14+3=17.
Q. 12
Intelligence Tests
Difficulty: Hard
(1 Mark)
A student has thrice as many wrong sums as he had right. If 32 in all, how many correctly?
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Step-by-Step Explanation & Concept Rationale
Let R be right: R+3R=32⟹4R=32⟹R=8.
Q. 13
Intelligence Tests
Difficulty: Hard
(1 Mark)
Ratio 1:5. Add 5 to each, becomes 1:4. Pair of numbers?
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Step-by-Step Explanation & Concept Rationale
x/5x=1/5; (x+5)/(5x+5)=1/4⟹4x+20=5x+5⟹x=15.
Q. 14
Intelligence Tests
Difficulty: Hard
(1 Mark)
Harpreet decreased by 20 and then added 20% to result. Final differed by 8. Number?
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Step-by-Step Explanation & Concept Rationale
Note: In standard percentage alertness tests, the phrasing "decreased by 20" means decreased by 20%.
Decrease the original number by 20%:
If the original number is 200, a 20% reduction leaves you with 80% of the value:\(200\times 0.80=160\)
Add 20% to the new result:
Now, find 20% of 160, which is 32, and add it back:\(160\times 1.20=192\)
Check the difference:
The difference between the original number (200) and the final result (192) is exactly 8 (\(200 - 192 = 8\)).
Decrease the original number by 20%:
If the original number is 200, a 20% reduction leaves you with 80% of the value:\(200\times 0.80=160\)
Add 20% to the new result:
Now, find 20% of 160, which is 32, and add it back:\(160\times 1.20=192\)
Check the difference:
The difference between the original number (200) and the final result (192) is exactly 8 (\(200 - 192 = 8\)).
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