General Aptitude Questions and Answers for Freshers for Competitive Exams

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.