### Important Mathematics for exam

1. Speed of a boat in still water is 16km/h. If it can travel 20km
downstream in the same time as it
can travel 12 km upstream, the rate of stream is.
a)1km/h
b)2km/h
c)4km/h
d)5km/h
Solution: Speed downstream: Speed upstream=20:12=5:3
Speed of current=5-3/5+3*16=4km/h

2. In one hour, a boat goes 11km along the stream and 5km against the
stream.
The speed of the boat in still water (in km/hr)is:
a)3
b)5
c)8
d)9
Solution: Speed in still water=1/2(11+5)kmph=8kmph

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If ratio of downstream and upstream speeds of a boat is ‘a:b.’
Then ratio of time taken= b:a
Speed of stream=a-b/a+b *Speed in still water
Speed in still water =a+b/a-b *Speed of stream

3. How many number of times will the digit '7' be written when listing the integers
from 1 to 1000?
A) 271
B) 300
C) 252
D)304

4. How many numbers are there between 100 and 1000 such that at least one of
their digits is 6?
A) 648
B) 258
C) 654
D)252

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PERMUTATION & COMBINATION
nPr = n!/ (n-r)!
nCr = n!/r!(n-r)!
nCr = nC(n-r)
nCr = nPr/r!
0!=1
1!=1
nPn=n!
nP1=n
nC1=n
nCn=1

Time & Work :
5. Pipe A can fill a tank in 'a' hours. On account of a leak at the bottom of the tank it takes thrice as
long to fill the tank. How long will the leak at the bottom of the tank take to empty a
full tank, when pipe A is kept closed?
A) (3/2)a hours
B) (2/3)a
C) (4/3)a
D) (3/4)a

6. Ram, who is half as efficient as Krish, will take 24 days to complete a work if he worked alone. If
Ram and Krish worked together, how long will they take to complete the work?
A) 16 days
B) 12 days
C) 8 days
D) 18 days

7. Two workers A and B manufactured a batch of identical parts. A worked for 2
hours and B worked for 5 hours and they did half the job. Then they worked together for another 3
hours and they had to do (1/20)th of the job. How much time does B take to complete the job, if he
worked alone?
A) 24 hours
B) 12 hours
C) 15 hours
D) 30 hours

TIME SPEED AND DISTANCE
Important Formula
1. Speed, Time and Distance:
Speed = Distance / time
Time = distance /speed
Distance =speed*time

AVERAGE: -

8. When a student weighing 45 kgs left a class, the average weight of the remaining
59 students
increased by 200g. What is the average weight of the remaining 59 students?
a) 57 kgs
b) 56.8 kgs
c)58.2 kgs
d)52.2 kgs

9. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the
ratio 1 : 1 : 2.
If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
a) Rs. 169.50
b) Rs. 170
c) Rs. 175.50
d) Rs. 18

10. A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How
much of the
mixture must be drawn off and replaced with water so that the mixture may be half
water and half syrup?
a) 1/3
b) 1/4
c) 1/5
d) 1/7