Numerical Ability Test - 22

Given:

Distance between city A and city B = 480 km

A car starts from A at (3/5) of its original speed and reaches B late by 80 minutes

Formula Used:

Time = Distance / Speed

Calculation:

Let the original speed of the car be x km/h

Original time taken = 480 / x hours

New speed = (3/5) × x = 3x/5 km/h

New time taken = 480 / (3x/5) hours

New time taken = 480 × (5/3x) hours

New time taken = 800 / x hours

New time taken is 80 minutes (or 80/60 = 4/3 hours) more than the original time taken

Therefore, 800 / x = 480 / x + 4/3

⇒ 800 / x - 480 / x = 4/3

⇒ (800 - 480) / x = 4/3

⇒ 320 / x = 4/3

⇒ 320 × 3 = 4x

⇒ 960 = 4x

⇒ x = 960 / 4

⇒ x = 240 km/h

The original speed of the car is 240 km/h.

Given:

In a 600 m race, A gave B a head start of 5 seconds and still won the race by 20 seconds.

The ratio of the speed of A to the speed of B is 2 ∶ 1.

Formula Used:

Speed = Distance / Time

Calculation:

Let the speed of B be x m/sec.

Then, the speed of A = 2x m/sec.

Time taken by A to cover 600 m = 600 / 2x

Time taken by B to cover 600 m = 600 / x

According to the question,

Time taken by B - Time taken by A = 25 sec (B had a head start of 5 seconds and lost by 20 seconds)

⇒ (600 / x) - (600 / 2x) = 25

⇒ 600(2 - 1) / 2x = 25

⇒ 600 / 2x = 25

⇒ 600 = 50x

⇒ x = 600 / 50

⇒ x = 12 m/sec

The speed of B is 12 m/sec.

Given:

Devendra leaves home at 8:25 am and reaches the office at 9:55 am every day. Therefore, the total time taken is:

9:55 am - 8:25 am = 1 hour 30 minutes (or 90 minutes).

On a particular day, he covers:

 3/10 of the total distance at 6/7 of his normal speed, and

 7/10 of the total distance at 7/6 of his normal speed.

To find: The time Devendra reaches the office on this particular day.

Solution:

Step 1: Normal time to cover the whole distance

Let the total distance be D and the normal speed be S.

The normal time taken to cover the entire distance is:

Time = D / S = 90 minutes

Step 2: Time for the first part of the journey (3/10 of the distance)

Distance for the first part = (3/10) × D

Speed for the first part = (6/7) × S

Time for the first part:

Time = (3/10 × D) / (6/7 × S)

Simplifying: Time = (3/10 × D) × (7/6 × 1/S) = (7/20) × (D / S)

Since we know D / S = 90 minutes from the normal time:

Time = (7/20) × 90 = 31.5 minutes

Step 3: Time for the second part of the journey (7/10 of the distance)

Distance for the second part = (7/10) × D

Speed for the second part = (7/6) × S

Time for the second part:

Time = (7/10 × D) / (7/6 × S)

Time = (7/10 × D) × (6/7 × 1/S) = (6/10) × (D / S)

Since we know D / S = 90 minutes from the normal time:

Time = (6/10) × 90 = 54 minutes

Step 4: Total time taken for the journey

Total time = Time for the first part + Time for the second part

Total time = 31.5 minutes + 54 minutes = 85.5 minutes

Step 5: Time Devendra reaches the office

Devendra leaves home at 8:25 am, and the time taken is 85.5 minutes (1 hour 25 minutes and 30 seconds).

Therefore, Devendra reaches the office at:

8:25 am + 1 hour 25 minutes 30 seconds = 9:50:30 am.

Answer: Devendra reaches the office at 9:50:30 am.

Given:

Train: 550 km at 55 km/h

Plane: 4500 km at 500 km/h

Boat: 400 km at 25 km/h

Auto: 55 km at 35 km/h

Formula Used:

Average speed = Total distance traveled / Total time taken

Calculation:

Total Distance = 550 + 4500 + 400 + 55

Total Distance = 5505 km

Time taken by Train = 550 / 55

Time taken by Train = 10 hours

Time taken by Plane = 4500 / 500

Time taken by Plane = 9 hours

Time taken by Boat = 400 / 25

Time taken by Boat = 16 hours

Time taken by Auto = 55 / 35

The average speed for the entire journey is 150¹³⁵⁄₂₅₆ km/h.

Given:

Total distance = 40 km

Speed of the first 10 km = 40 km/h

Time for the first 10 km = 2 × Time for the second 10 km

Time for the fourth 10 km = Time for the first 10 km

Time for the third 10 km = 1/2 × Time for the fourth 10 km

Formula used:

Average speed = Total distance/Total time

Calculations:

Required time for the first 10 km = 10/40 = 1/4 hr.

Now,

Required time for the first 10 km = 2 × Required time for the second 10 km

⇒ Required time for the second 10 km = (Required time for the first 10 km)/2

So, Required time for the second 10 km = (1/4)/2 = 1/4 × 1/2 = 1/8 hr.

According to the given data,

Required time for the fourth 10 km = 1/4 hr.

So, required time for the third 10 km = 1/4 × 1/2 = 1/8 hr.

Now, average speed = (10 + 10 + 10 + 10)/(1/8 + 1/4 + 1/4 + 1/8) 

⇒ 40/(6/8) = 40/(3/4) = 40 × 4/3 = 160/3 km/h

∴ The average speed is 160/3 km/h.

Given:

Walking at 3/4 of her normal speed Tanvi takes 2 hours more than the normal time.

Calculations:

By walking 3/4 of usual speed, Tanvi takes 2 hours more than the normal time.

∴ With a speed of 3/4 of usual speed, the time taken is 4/3 of usual time

Let T be the usual time

⇒ {(4/3) × T} – T = 2 hours

⇒ T = 6 hours

∴ The required value of time is 6 hours.

Given:

A car traveling at a speed of 70 km/h

Overtakes a bus traveling in the same direction and leaves it 170 m behind in 18 seconds.

Formula used:

Concept used:

When the two objects move in the same direction, the Speed of both is subtracted from each other.

We have to change the speed km/h to meter for this We have to multiply with 5/18

Calculation:

Let the speed of the bus = y km/h

⇒ (70 - y) = 170/5

⇒ 70 - y = 34

⇒ y = 36

∴ The speed of the bus is 36 km/h

Given:

Distance between policeman and thief = 68 meters.

Speed of policeman & thief = 4 m/s and 9 m/s respectively

Formula Used:

Time taken = Distance/Speed

Relative speed = (a - b) km/hr

Where, a = speed of a policeman & b = speed of a thief

Calculation:

Relative speed = (9 - 4) m/s = 5 m/s

Time taken for the policeman to catch the thief = 68/5 = 13.6 seconds.

Hence, the correct answer is 13.6 seconds.

Given:

Ratio of the boat in still water & speed of stream = 10 : 6 

Distance covered by downstream = 42 km

Distance covered by upstream  = 34 km

Total time taken = 6 hours

Concept used:

Downstream speed(DS) = Speed of the boat in still water(SW)  + Speed of the stream(V)

Upstream speed(US) = Speed of the boat in still water(SW)  -  Speed of the stream(V)

Formula used:

Time = Distance/ speed

(DS/ SW + V) + (US/ SW - V) = Total time

Calculation:

Let the speed of boat in still water and speed of stream be '10x'  & '6x' km/hrs respectively.

Downstream speed = 16x ( 10 + 6 )

Upstream speed = 4x ( 10 - 6 )

Now, according to the question

⇒ (42 /16x) + (34 /4x) = 6

⇒ (21 /8x) + (17 /2x) = 6 

⇒ 21 + 68 / 8x = 6 

⇒ 89  = 48x

⇒ x = 89/48

⇒ Downstream speed = 16x = 16 × 89/48 km/hrs

⇒ 29.66 km/hrs

∴ Downstream speed is 29.66 km/hrs

Given:

Length of Mumbai Rajdhani (L1) = 850 m

Length of kissan express (L2) = 700 m

Distance between the trains (D) = 1050 m

Speed of Mumbai rajdhani (V1) = 62 km/h = 17.22 m/s

Speed of kissan express (V2) = 55 km/h = 15.28 m/s

Formula used:

Time = Distance / Relative speed

Relative speed = V1 + V2

Calculation:

Relative speed = 17.22 m/s + 15.28 m/s = 32.50 m/s

Now, to find the time taken for the trains to cross each other, we use the formula:

Time = (Length of Mumbai Rajdhani + Length of Kissan Express + Distance between them) / Relative speed

⇒ (850 + 700 + 1050) / 32.50

⇒ 2600 / 32.50 = 80 seconds

∴ The trains will cross each other in approximately 80 seconds.