** **

**1)A train covers a distance in 50 min ,if it runs at a speed**

**of 48kmph on an average.The speed at which the train must run**

**to reduce the time of journey to 40min will be.**

**1. Solution::**

Time=50/60 hr=5/6hr

Speed=48mph

distance=S*T=48*5/6=40km

time=40/60hr=2/3hr

New speed = 40* 3/2 kmph= 60kmph

**2)Vikas can cover a distance in 1hr 24min by covering 2/3 of**

**the distance at 4 kmph and the rest at 5kmph.the total**

**distance is?**

**2. Solution::**

Let total distance be S

total time=1hr24min

A to T :: speed=4kmph

diistance=2/3S

T to S :: speed=5km

distance=1-2/3S=1/3S

21/15 hr=2/3 S/4 + 1/3s /5

84=14/3S*3

S=84*3/14*3

= 6km

**3)walking at . of his usual speed ,a man is late by 2 . hr.**

**the usual time is.**

**3. Solution::**

Usual speed = S

Usual time = T

Distance = D

New Speed is . S

New time is 4/3 T

4/3 T – T = 5/2

T=15/2 = 7 .

**4)A man covers a distance on scooter .had he moved 3kmph**

**faster he would have taken 40 min less. If he had moved**

**2kmph slower he would have taken 40min more.the distance is.**

**4.Solution::**

Let distance = x m

Usual rate = y kmph

x/y – x/y+3 = 40/60 hr

2y(y+3) = 9x ————–1

x/y-2 – x/y = 40/60 hr y(y-2) = 3x —————–2

divide 1 & 2 equations

by solving we get x = 40

**5)Excluding stoppages,the speed of the bus is 54kmph and**

**including stoppages,it is 45kmph.for how many min does the bus**

**stop per hr.**

**5.Solution::**

Due to stoppages,it covers 9km less.

time taken to cover 9 km is [9/54 *60] min = 10min

6)Two boys starting from the same place walk at a rate of

5kmph and 5.5kmph respectively.wht time will they take to be

8.5km apart, if they walk in the same direction

**6.Solution::**

The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph

Distance between them is 8.5 km

Time= 8.5km / 0.5 kmph = 17 hrs

**7)2 trains starting at the same time from 2 stations 200km**

**apart and going in opposite direction cross each other ata**

**distance of 110km from one of the stations.what is the ratio of**

**their speeds.**

**7. Solution::**

In same time ,they cover 110km & 90 km respectively

so ratio of their speed =110:90 = 11:9

**8)Two trains start from A & B and travel towards each other at**

**speed of 50kmph and 60kmph resp. At the time of the meeting the**

**second train has traveled 120km more than the first.the distance**

**between them.**

**8. Solution::**

Let the distance traveled by the first train be x km

then distance covered by the second train is x + 120km

x/50 = x+120 / 60

x= 600

so the distance between A & B is x + x + 120 = 1320 km

**9)A thief steals a ca r at 2.30pm and drives it at 60kmph.the**

**theft is discovered at 3pm and the owner sets off in another car**

**at 75kmph when will he overtake the thief**

**9. Solution::**

Let the thief is overtaken x hrs after 2.30pm

distance covered by the thief in x hrs = distance covered by

the owner in x-1/2 hr

60x = 75 ( x- .)

x= 5/2 hr

thief is overtaken at 2.30 pm + 2 . hr = 5 pm

**10)In covering distance,the speed of A & B are in the ratio**

**of 3:4.A takes 30min more than B to reach the destion.The time**

**taken by A to reach the destinstion is.**

**10. Solution::**

Ratio of speed = 3:4

Ratio of time = 4:3

let A takes 4x hrs,B takes 3x hrs

then 4x-3x = 30/60 hr

x = . hr

Time taken by A to reach the destination is 4x = 4 * . = 2 hr

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