7000+ Royal Bank of Scotland Aptitude Test Questions and Answers - 1

Ans: C

Speed of first train = $$({150}/{15})$$ m/sec = 10 m/sec.

Let the speed of second train be x m/sec.

Relative speed = (10 + x)m/sec.

∴ $${300} / {10 + x}$$ = 12 ⇔ 300 = 120 + 12x

⇔ 12x = 180

⇔ x = $${180} /{12}$$ = 15 m/sec.

Hence, speed of other train = $$(15 × {18}/{5})$$ kmph = 54 kmph.

Ans: B

Let the length of the first train be x metres.

Then, the length of second train is $$({x}/{2})$$ metres.

Relative speed = (48 + 42) kmph = $$(90 × {5}/{18})$$ m/sec = 25 m/sec.

∴ $$(x + {x}/{2}) / {25}$$ = 12 or $${3x}/{2}$$ = 300 or x = 200.

∴ Length of first train = 200 m.

Let the length of platform be y metres.

Speed of the first train = $$(48 × {5}/{18})$$ m/sec = $${40}/{3}$$ m/sec.

∴ (200 + y) × $${3}/{40}$$ = 45

⇔ 600 + 3y = 1800 ⇔ y = 400 m.

Ans: C

Speed = $$(54 × {5}/{18})$$ m/sec = 15 m/sec.

Length of the train = (15 × 20) m = 300 m.

Let the length of the platform be x metres.

Then, $${x + 300} / {36}$$ = 15 ⇔ x + 300 = 540 ⇔ x = 240 m.

Ans: C

Speed = $$(30 × {5}/{18})$$m/sec = $$({25}/{3})$$m/sec.

Time = 36 sec.

Let the length of the bridges be x metres.

Then, $${50 + x} / {36}$$ = $${25} / {3}$$ ⇔ 3 (50 + x) = 900

⇔ 50 + x = 300 ⇔ x = 250 m.