The speed of a car is 60% more than the speed of a bus. The train can cover ( d + 850) km distance in ( t + 8) hours. The car covers (d-366) km distance in (t – 2) hours. The speed of train is 2.5 times the speed of bus. The distance travelled by bus is 640 km in which it will take ( t + 8 ) hours, then which of the following statements are true?

1. Unit digit of d is non – zero value
2. ‘t’ is perfect cube number.
3. In (t-2.5) hours car travel 352 km.

Calculation:

Let speed of bus is 100s,

Then speed of car 100s × 160 /100 = 160s

Speed of train 100s × 2.5 = 250s

250s × [t +8] = [d + 850] –---(I)

160s × [t -2] = [d – 366] ---(II)

100s × [t + 8] = 640 -----(III)

By doing equation  I  divided  III,

5/2 = [d + 850] /640

Or, d = 1600 – 850 = 750

From I and II,

25 ×  [t + 8 ] / 16 × [t -2] = [750 + 850]/[750 - 850]=1600/384

Or, 3t + 24 = 8t -16

Or, 5t = 40

Or, t = 40 /5 = 8

From II,  [750 – 366] / 6 = 160s

Or, s = 64/160

So, speed of car = 160s = 64/160 × 160 = 64 km / hr

1) Unit digit of d is non – zero value.

As d = 750

⇒ It is false

2) ‘t’ is perfect cube number.

⇒ t = 8 ( cube of 2)

it is true.

3) In (t-2.5) hours car travel 352 km.

Distance travel by car = speed of car × time 

⇒ [8-2.5] ×  64 = 352.

It is true.

So, only II and III true.