Aptitude Math Questions for SSC Exams
Anuja owns $$66{2\over 3}\%$$ of a property. If 30% of the property that she owns is worth 1,25,000, then 45% of the value (in) of the property is:
(A) 2,70,000
(B) 2,81,250
(C) 2,25,000
(D) 2,62,500
Correct Answer : B
If the radius of the base of a right circular cylinder is increased by 20% and the height is decreased by 30%, then what is the percentage increase/decrease in the volume?
(A) Decrease 0.8%
(B) Increase 2%
(C) Increase 0.8%
(D) Decrease 2%
Correct Answer : C
Rishu saves x% of her income. If her income increases by 26% and the expenditure increases by 20%, then her savings increase by 50%. What is the value of x?
(A) 25
(B) 30
(C) 20
(D) 10
Correct Answer : C
A certain number of students from school X appeared in an examination and 30% students failed. 150% more students than those from school X, appeared in the same examination from school Y. If 80% of the total number of students who appeared from X and Y passed, then what is the percentage of students who failed from Y?
(A) 24
(B) 20
(C) 16
(D) 18
Correct Answer : C
If 20% of (A + B) = 30% of (A − B), then what percentage of B is equal to A?
(A) 400%
(B) 300%
(C) 500%
(D) 100%
Correct Answer : C
A and B start moving towards each other from places X and Y, respectively, at the same time on the same day. The speed of A is 20% more than that of B. After meeting on the way, A and B take p hours and 72 hours, respectively, to reach Y and X, respectively. What is the value of p?
(A) 4.5
(B) 5
(C) 5.5
(D) 6
Correct Answer : B
A person has to cover a distance of 160 km in 15 hours. If he covers $${4\over 5}$$ of the distance in $${2\over 3}$$ of the time, then what should be his speed (in km/h) to cover the remaining distance in the remaining time?
(A) 6
(B) 8
(C) 6.4
(D) 6.5
Correct Answer : C
Neena was cycling to the market to buy some grocery items. The market is 4 km away from her home. She travels at a speed of 12 km/h for first 10 minutes. On her way she meets her friend Nikhat and stops to chat with her for 15 minutes. She resumes her journey at a speed of 8 km/h. What is her average speed for the journey ?
(A) 6 km/h
(B) 8 km/h
(C) 10 km/h
(D) 4 km/h
Correct Answer : A
Reshma covers 45 km at a speed of 15 km/h by bicycle, 80 km at a speed of 40 km/h by car, and another 6 km at a speed of 2 km/h on foot. Find her average speed for the whole journey (correct to 2 decimal places).
(A) 16.38 km/h
(B) 43.50 km/h
(C) 18.36 km/h
(D) 15.25 km/h
Correct Answer : A
Akhil takes 30 minutes extra to cover a distance of 150 km if he drives 10 km/h slower than his usual speed. How much time will he take to drive 90 km if he drives 15 km per hours slower than his usual speed?
(A) 2h 45m
(B) 2h 30m
(C) 2h
(D) 2h 15m
Correct Answer : C
Explanation :
Let's use the information given to calculate Akhil's usual speed first.
We know that Akhil takes 30 minutes (0.5 hours) extra to cover a distance of 150 km when he drives 10 km/h slower than his usual speed.
Let "S" be Akhil's usual speed in km/h. So, his slower speed would be (S - 10) km/h.
The time taken to cover a distance is equal to the distance divided by the speed: Time = Distance / Speed
At his usual speed, it takes him: Time at usual speed = 150 km / S hours
At the slower speed, it takes him: Time at slower speed = 150 km / (S - 10) hours
The difference in time between these two scenarios is 0.5 hours (30 minutes): Time at slower speed - Time at usual speed = 0.5 hours
Now, we can set up the equation and solve for S:
(150 km / (S - 10)) - (150 km / S) = 0.5
To solve this equation, we'll first get a common denominator: [150S - 150(S - 10)] / [S(S - 10)] = 0.5
Now, simplify and solve for S: [150S - 150S + 1500] / [S(S - 10)] = 0.5
1500 / [S(S - 10)] = 0.5
Now, cross-multiply: 2 * 1500 = S(S - 10)
3000 = S^2 - 10S
S^2 - 10S - 3000 = 0
Now, we can solve this quadratic equation for S using the quadratic formula:
S = [-(-10) ± √((-10)^2 - 4(1)(-3000))] / (2(1))
S = [10 ± √(100 + 12000)] / 2
S = [10 ± √12100] / 2
S = [10 ± 110] / 2
Now, we have two possible values for S, but we'll take the positive one because speed cannot be negative:
S = (10 + 110) / 2 = 120/2 = 60 km/h
So, Akhil's usual speed is 60 km/h.
Now, we want to find out how much time he will take to drive 90 km when he drives 15 km/h slower than his usual speed, which would be (60 - 15) = 45 km/h.
Time = Distance / Speed Time = 90 km / 45 km/h = 2 hours
Akhil will take 2 hours to drive 90 km when he drives 15 km/h slower than his usual speed.
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Rajesh Bhatia
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