Model 5 Train Vs Both platform and a man/a pole Practice Questions Answers Test with Solutions & More Shortcuts

Question : 16 [SSC CGL Tier-I 2014]

A train leaves a station A at 7 am and reaches another station B at 11 am. Another train leaves B at 8 am and reaches A at 11.30 am. The two trains cross one another at

a) 8:56 am

b) 9:00 am

c) 9:24 am

d) 8:36 am

Answer: (c)

Let both trains meet after t hours since 7 a.m.

Distance between stations A and B = x Km.

$x/4 × t + x/{7/2} × (t - 1) = x$

[Speed = $\text"Distance"/ \text"Time"$]

$t/4 + {2(t - 1)}/7$ = 1

${7t + 8t - 8}/28$ = 1

15 t - 8 = 28

15 t = 28 + 8 = 36

t = $36/15 = 12/5$ hours

= 2 hours 24 minutes

∴ Required time = 9 :24 a.m.

Question : 17 [SSC Delhi Police S.I.2012]

Points 'A' and 'B' are 70 km apart on a highway. A car starts from 'A' and another from 'B' at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each-other, they meet in one hour. Find the speed of the two cars (in km/hr).

a) 40, 30

b) 30, 50

c) 20, 40

d) 20, 30

Answer: (a)

Let speed of car starting from A be x kmph

and speed of car starting from B be y kmph

Case I

When cars meet at P,

7x = AP = AB + BP = 70 + 7y

7x - 7y = 70

x - y = 10 ...(i)

Case II

When cars meet at Q,

x + y = 70 ...(ii)

On adding these equations,

x = 40 kmph

Putting the value of x in equation (i),

y = 40 - 10 = 30 kmph

IMPORTANT quantitative aptitude EXERCISES

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