# Exercise : 5

(b) 50 m

(c) 54 m

(d) 72 m

(e) None of these

**Ans.b**

Let actual speed of train = S m /sec

and length of train = L m.

Then, S - \(\frac{2 \times 5}{18} = \frac{L}{9}\)

⇒ 9S = L + 5 ...… (i)

and S - 4 × ^{5}⁄_{18} = ^{L}⁄_{10}

⇒ 90S = 9L + 100 .....(ii)

By (i) & (ii), we get L = 50 m.

(b) 3.5 km/h

(c) 4.5 km/h

(d) 3 km/h

(e) None of these

**Ans.a**

Let speed of man = S km/h. Then,

Distance covered in 15 min = Distance covered in 12 min

16 × ^{15}⁄_{60} = ^{12}⁄_{60}[16 + S]

⇒ 16 + S = 20 ⇒ S = 4 km/h

(b) 7 km/h

(c) 6 km/h

(d) 5.8 km/h

(e) None of these

**Ans.a**

Let speed of man = S km/h. Then,

36 × ^{14}⁄_{60} = ^{18}⁄_{60}[36 - S] ⇒ 36 – S = 28 ⇒ S = 8 km/h.

(b) 72 km/h

(c) 78 km/h

(d) 81 km/h

(e) None of these

**Ans.d**

4.5 km/h = (4.5 × ^{5}⁄_{18}) m/sec = 1.25 m/sec.

& 5.4 km/h = (5.4 × ^{5}⁄_{18}) m/sec = 1.5 m/sec.

Let the speed of the train be S m/sec.

Then, (S – 1.25) × 8.4 = (S – 1.5) × 8.5

⇒ 8.4S – 10.5 = 8.5S – 12.75 ⇒ 0.1S = 2.25 ⇒ S = 22.5.

∴ Speed of the train = (22.5 × ^{18}⁄_{5}) km/h = 81 km/h

(b) 3 : 2

(c) 3 : 4

(d) 2 : 1

(e) None of these

**Ans.b**

Let the speeds of the two trains be S_{1} m/sec and S_{2} m/sec respectively. Then, length of the first train = 27S_{1} metres, and length of the second train = 17S_{2} metres.

∴ \(\frac{27S_{1} + 17S_{2}}{S_{1} + S_{2}} = 23 \) ⇒ 27S_{1} + 17S_{2} = 23S_{1} + 23S_{2}

⇒ 4S_{1} = 6S_{2} ⇒ ^{S1}⁄_{S2} = ^{3}⁄_{2}

(b) 3 s

(c) 4 s

(d) 5 s

(e) None of these

**Ans.c**

Relative speed of the trains = (40 + 20) = 60 m/s

Distance = (120 + 120) = 240 m

Time taken by trains to cross each other completely

= ^{240}⁄_{60} 4s

Directions (Qs. 7 - 8): Answer the following questions on the basis of the information given below:

(i) Trains A and B are travelling on the same route heading towards the same destination. Train B has already covered a distance of 220 km before train A started.

(ii) The two trains meet each other 11 hours after the start of train A.

(iii) Had the trains been travelling towards each other (from a distance of 220 km), they would have met after one hour.

(b) 180

(c) 116

(d) Data inadequate

(e) None of these

**Ans.a**

Let the speeds of train A and B be V_{A} and V_{B} respectively.

V_{A} - V_{B} = ^{220}⁄_{11} ⇒ ^{220}⁄_{11} ⇒ V_{A} - V_{B} = 20 ......(i)

V_{A} + V_{B} = ^{220}⁄_{1} ⇒ V_{A} + V_{B} = 220 .......(ii)

Solving the equations (i) and (ii), we get V_{A} = 120 km/hr and V_{B} = 100 km/hr

(b) 80.5

(c) 118

(d) Data inadequate

(e) None of these

**Ans.e**

Let the speeds of train A and B be V_{A} and V_{B} respectively.

V_{A} - V_{B} = ^{220}⁄_{11} ⇒ ^{220}⁄_{11} ⇒ V_{A} - V_{B} = 20 ......(i)

V_{A} + V_{B} = ^{220}⁄_{1} ⇒ V_{A} + V_{B} = 220 .......(ii)

Solving the equations (i) and (ii), we get V_{A} = 120 km/hr and V_{B} = 100 km/hr