1] How many pieces each of length 4.5 m can be cut out from 225 m of wire?
a]50 b]51 c]52 d]53

number of pieces = 225/4.5 = 50

2] How many pieces each of length 3.5 m can be cut out from 15 m of cloth?
a]4.285 b]4.28 c]4.2 d]none

3] How many pieces each of length 85 cm can be cut out from 42.5 m of rod?
a]50 b]51 c]52 d]53

4] How many pieces each of length 3/7 m can be cut out from 2(4/7) m roll of ribbons?
a]6 b]5 c]2 d]3

5] How many scarfs each of length 3.5 sq.m long can be cut out from 15 m area of cloth?
a]25 b]21 c]22 d]23

6] A pile of metal sheets is 39.9 cm in height.If each sheet is 0.7 cm thick,how many sheets are there in the pile?
a]57 b]51 c]52 d]53

1]Bread contains 0.06 part of protein by weight.A patient requires 42 grams of protein per day.How many grams of bread are required by the patient?
a]700 b]600 c]500 d]400
number of grams = 42/ 0.06 = 700

1] A man has some hens and cows.If the number of heads be 48 and the number of feet equals 140.Then the number of hens will be
a]22 b]23 c]24 d]26

let the number of hens be x
let the number of cows be y

x+y= 48
2x + 4y = 140 = > x+2y = 70

x+y= 48
x+2y = 70
-------------
y = 22

x+22 = 48
x = 26

2] There are deer and peacocks ina  zoo.By counting the heads they are 80.The number of their legs is 200.How many peacocks are there?
a]60 b]63 c]64 d]66


2] There are lions and parrots in a  zoo.By counting the heads they are 15.The number of their legs is 50.How many lions are there?
a]10 b]13 c]14 d]16

1]A is thrice as good a workman as B and therefore it is able to finish a job in 60 days less than B.Working together they can do it in
a]20 days b]22 (1/2) days c]25 days d]30 days

ratio of time taken by A and B is 1:3
let days taken by A and B is x and 3x
difference = 2x
2x = 60
x = 30
Days taken by A and B is 30 and 90
total time taken if they work together = 1/30 + 1/90 = 22(1/2) days

2]A is 6 times as fast as B and takes 100 days less to complete a work than B.Find the total number of days taken by A and B to complete the work.
a]17 days b]17(1/2) days c]18 days d]19 days

1]The banker's discount on Rs.1800 at 12% per annum is equal to the true discount on Rs.1872 for the same time at the same rate.Find the time
a]1/3 years b]2/3 years c]4/3 years d]5/3 years

SI on Rs.1872
preset worth of Rs.1872 is 1800
SI on Rs1800 at 12%  = [1872-1800] = 72
SI = PTR/100
72 =( 1800* T * 12)/100
T = 1/3 years

1] A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 150 m long, find its speed.
a] 10 kmph b]20 kmph c]30 kmph d]40kmph

Sol. Relative speed = (150/9) m/sec =(150/ 9 x 18/5) kmph = 60 kmph.
:. Speed of goods train = (60 - 50) kmph = 10 kmph.

2] A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.
a] 12 kmph b]22 kmph c]42 kmph d]62 kmph

1] A train 140 m long is running at 60 kmph. In how much time will it pass a platform 260 m long?
a] 98 s b]24 s c]12 s d]14 s

Sol. Speed of the train = (60 x 5/18) m/sec =50/3m/sec.
       Distance covered in passing the platform = (140 + 260) m = 400 m
       :. Time taken = (400 x 3/50) see = 24 sec.

2] How long does a train 110 metres long running at the speed of 72 km/hour take to cross a bridge 132 metres in length.
a] 9.8 s b]12.1 s c]12.42 s d]14.3 s

1]Find the time taken by a train 180 m long, running at 72 kmph,in crossing an electric pole.
a] 9 s b]8 s c]7 s d]6 s

Sol. Speed of the train = (72 x 5/18) m/sec = 20 m/sec.
Distance moved in passing the pole = 180 m.
Required time taken = (180/20) sec = 9 sec.

2]In what time will a train 100 m long cross an electric pole,if its speed be 144 km/hr?
a] 2.5 s b]4.25 s c]5 s d]12.5 s

1]A dairy man pays Rs.6.4 per litre of milk.He adds water and sells the mixture at Rs.8 per litre,thereby making 37.5% profit.The proportion of water to milk recieved by the customers is
a]10:1 b]10:2 c]10:3 d]10:4

required ratio of the water and the milk in the mixture = x:y
CP of x litres of milk = Rs.6.4 x
SP of x litres of milk = Rs. 8(x+y)
profit % = 37.5
gaint % =( sp/cp *100) - 100
37.5 = [{8(x+y) } /64.x ]* 100 - 100
137.5/100 = (8x + 8y )/6.4x
880x - 800x = 800y
80x = 800 y
x/y = 10:1

1] A man sells an article at 5% profit.If he had brought it at 5% less and sold it for Re.1 less,he would have gained 10%.The cost price of the article is what?
a]100 b]200 c]300 d]400

let the cost price of the article be Rs. x
profit = 5%
selling price = x+(5% of x) = 21x/20
cost price = x - (5% of x) = 95/100
If sold for Rs.1 less
SP = [(21x/20) - 1].Then gain % is 10

{(New SP - SP)/ SP} * 100 = 10
{(2x-20)/19x} *100  = 10
2x-20 = 19x /10
20x - 200 = 19x
x = 200

1]A box of light bulbs contains 24 bulbs.A worker replaces 17 bulbs in the shipping department and 13 bulbs in the accounting department.How many boxes of bulbs did the worker use?
a]1 (1/4) b]2 (1/4) c]1 (3/4) d]1 (5/4)

24 bulbs in 1 box
replaced bulbs = 17+13 = 30
number of boxes of bulbs the worker used = 30/24 = 1 (1/4)

1]A single discount of 10%,20% and 40% is equal to a single discount of

a]50% b]56.8% c]60% d]70.28%
Net SP = [100-40%] of [100-20%] of [100-10%] of Rs.100
            = 60% of 80% of 90% of Rs.100
            = 60/100 * 80/100 * 90/100 * 100
            = 43.2
Required discount = 100 - 43.2 = 56.8

2]A single discount of 10%,20% and 5% is equal to a single discount of
a]31.6% b]31.5% c]31.4% d]31.3%

3]A single discount of 10%,12% and 15% is equal to a single discount of
a]50.2% b]67.32% c]60.8% d]70.28%

4]A single discount of 30% and 10% is equal to a single discount of
a]50% b]56% c]63% d]70%

5]A single discount of 20% and 30% is equal to a single discount of
a]50% b]56% c]60% d]70%

6]Two successive discounts of 20% and 15% are qual to a single discount of
a]50% b]68% c]60% d]70%

5]Two successive discounts of 20% and 10% are qual to a single discount of
a]50% b]56% c]60% d]72%

1]By selling a book for Rs.144 a shopkeeper loses 10%.At what price should he sell it inorder to gain 15%?
a]Rs.172 b]Rs.180 c]Rs.184 d]Rs.190

SP with CP as Rs.100 = 90 as there is 10 % loss
New SP with CP as Rs.100 = 115 as he needs 15% gain
SP with CP as Rs.100 : actual SP =New SP with CP as Rs.100 : New SP
 90 : 144 = 115 : x
90 x = 114 * 115
x = 184

2]By selling a watch for Rs.144 a shopkeeper loses 10%.At what price should he sell it inorder to gain 10%?
a]Rs.172 b]Rs.180 c]Rs.176 d]Rs.190

3] There would be 10% loss if rice is sold at Rs.5.50 per kg.At what price per kg should it be sold to earn a profit of 20%
a]Rs.7.20 b]Rs.7.02 c]Rs.7.33 d]Rs.6

4]A fruit seller sells mangoes at the rate of Rs.9/kg and thereby loses 20%.At what price per kg,he should have sold them to make a profit of 5%?
a]Rs.11.82 b]Rs.11.84 c]Rs.11.81 d]Rs.11.83

 5]When a plot is sold for Rs.18700 the owner loses 15%.At what price must the plot be sold in order to gain 15%?
a]Rs.2100 b]Rs.22500 c]Rs.25300 d]Rs.25800

1]How long does a train 110 mts long running at the speed of 132 km/hr take to cross a bridge 165 mts in length?
a]7.5 s b]7.4 s c]7.3 s d]7.2 s

solution
speed of train = d/t = (132*1000)/3600 m/s = 110/3 m/s
total distance covered = (110+165) = 275 m
time taken = [110/3] /275 = 7.5 s

2]How long does a train 110 mts long running at the speed of 72 km/hr take to cross a bridge 132 mts in length?
a]12.1 s b]12.4 s c]12.3 s d]12.2 s

3]A train is moving at a speed of 45 km/hr.If the lenght of the train is 360 mts.How long will it take to cross a bridge 140 mts in length?
a]40 s b]70 s c]30 s d] 20 s

4]How long does a train 110 mts long running at the speed of 36 km/hr take to cross a bridge 132 mts in length?
a]24.2 s b]24.4 s c]24.3 s d]24.2 s

1] A fruit seller loses 10% by selling mangoes at 26 for Rs.5.How many should he sell for a rupee to gain 17.4%?
a] 33.8 b]33.7 c]33.6 d]33.5

let the SP of 26 mangoes be Rs.X
If 10% money lost remaining is Rs.90

90:1 = 117 : x
90x = 117
x = 1.3
if for Rs. 1.3 mangoes sold is 26
For Re.1 mangoes sold = y

1.3 * y = 26 * 1
y = 33.8 Rs

2. By selling 45 lemons for Rs. 40, a man loses 20%. How many should he sell for Rs. 24 to gain 20% in the transaction?
a] 19 b] 18 c] 24 d] 22

1] A worker makes a basket in 2/3 of an hour.If he works for 7(1/2) hours,how many baskets can be made?
a]11(1/4) b]11(1/2) c]11(1/3) d]11(1/5)

[7(1/2) ]/ (2/3) = (15/2) / (2/3 ) = 45/4 = 11(1/4)

A company has 6435 bars of soap.If the company has sold 20% of its stock.How many bars of soap did it sell?
a]1287 b]1286 c]1285 d]1284

solution
20 % of 6435 = (20/100) * 6435 = 1287

1] A train can travel 20% faster than car.Both start from point A at the same time and reach point B 75 kms away from A at the same time.On the way however the train lost about 12.5 minutes while stopping at the stations.The speed of the car is

Solution
Let the speed of the car is x km/hr
speed of the train is x + 20% of x = (6x) / 5 km/hr



5 / (6x) * 75 + 25 / (2* 60) = 75/x
 375 / 6x + 5/24 = 75/x
375 / 6x - 75/x= - 5/24
-[80/6x] = - 5/24
  x = 60

1] A starts 3 minutes after B for a place 4.5 km distant. B on reaching his destination immediately returns and after walking a km meets A.If A can cover 1km in 18 mins what is B's speed?
a]6 km/hr b]7 km/hr c]8 km/hr d] 5 km/hr

A covers 3.5 km before meeting B.So time taken for it is =  [18 * 3.5] + 3 = 66 mins
B covers 5.5 km [11/2 km] before meeting A in 66 mins i.e., [66/60] hours = time taken

B's speed = [d/t] = [ 11/2 ]/ [11/10] = 5 km/hr

1] The sum of 6th and 15th elements of an AP is equal to the sum of space 7th,10th and 12th elements of the same progression.Which element of the series whould be equal to zero?
a]8th b]9th c] 11th d] 13th

solution
(a+5d) + (a+7d) = (a+6d) + (a+9d) + (a+11d)
2a+19d = 3a + 26d
a = -7d

T[8] = a+7d = -7d +7d = 0

1] A worker makes a basket in [2/3] of an hour.If he works for 7(1/2) hours,how many baskets will he make?
a]11(1/4) b]11(3/4) c]11(5/4) d] 11(6/4)

solution
{7(1/2)}/ (2/3) = (15/2) / (2/3) = 11(1/4)

1] Find the area of the traingle given the base and the corresponding altitude are 55mm and 34mm.
a] 931 b]932 c]933 d]935

area of the traingle = (1/2) * base * height = (1/2) *55*34 = 935 sq mm

2] Find the area of the triangle given the base and the corresponding altitude are 3.5mm and 2.4mm.
a] 4.1 b]4.2 c]4.3 d]4.5

3] Find the area of the triangle given the base and the corresponding altitude are 16.7mm and 10.9mm.
a] 91.015 b]91.014 c]91.014 d]91.013

a] The average of 30 results is 20 and the average of other 20 results is 30. What is the average of all the results?
a] 24 b] 48 c] 25 d] 50

Total numbers for in average of 30 results = 30*20 = 600
Total numbers for in average of 20 results = 20*30 = 600
Total numbers = 30+20

average of all the results = 600+600 /500 = 24

1] A mixture contains milk and water in the ratio 5:1.On adding 5 litres of water,the ratio of milk and water becomes 5:2.The quantity of milk in the mixture is
a]16 litres b]25 litres c]32.5 litres d]22.75 litres

5x/(x+5) = 5/2
10x = 5x+25
5x = 25
x = 5

quantity of milk = 5x = 25 litres

2] A mixture contains alcohol and water in the ratio 4:3.On adding 5 litres of water,the ratio of alcohol and water becomes 4:5.The quantity of alcohol in the mixture is
a]16 litres b]10 litres c]2.5 litres d]25 litres

1] A man can row downstream at 14 kmph and upstream at 9 kmph.Man's rate in still water is
a]5 kmph b]23 kmph c] 11.5 kmph d] none

rate in still water is = (1/2)(14+9) = 23/2 = 11.5 kmph

2] A man can row upstream at 7 kmph and downstream at 10 kmph.Man's rate in still water is
a]5 kmph b]23 kmph c] 8.5 kmph d] none

3] If a man can swim downstream at 6 kmph and upstream at 2 kmph.Man's rate in still water is
a]5 kmph b]23 kmph c] 4 kmph d] none

4] A man can row upstream at 11 kmph and upstream at 16 kmph.Man's rate in still water is
a]5 kmph b]23 kmph c] 13.5 kmph d] none

5] In one hour a boat goes 11km along the stream and 5 kmph against the stream.The speead of the boat in still water is
a]5 kmph b]23 kmph c] 11.5 kmph d] none

1]A man can row upstream at 11 kmph and downstream at 8 kmph.The speed of the stream is
a]3kmph b]9.5 kmph c]1.5 kmph d]6 kmph

speed of stream= (1/2) (11-8) = 3/2 = 1.5 kmph

2]A man can row upstream at 8 kmph and downstream at 13 kmph.The speed of the stream is
a]3kmph b]9.5 kmph c]2.5 kmph d]6 kmph

3]A man can row upstream at 6 kmph and downstream at 4 kmph.The speed of the stream is
a]1 kmph b]9.5 kmph c]1.5 kmph d]6 kmph

4]A man can row upstream at 14 kmph and downstream at 9 kmph.The rate of the current is
a]3kmph b]9.5 kmph c]2.5 kmph d]6 kmph

5]A man can row upstream at 11 kmph and downstream at 16 kmph.The speed of the stream is
a]3kmph b]9.5 kmph c]2.5 kmph d]6 kmph

6]A man can row upstream at 8 kmph and downstream at12 kmph.The rate of current is
a]2 kmph b]9.5 kmph c]1.5 kmph d]6 kmph

1] The fathers age was 5 times his son's age 5 years ago and will be 3 times son's age after 2 years. The ratio of their present ages is
a] 5:2 b]5:3 c]10:3 d]11:5

let son's age be 5 years ago be x and father's age 5x
After 5 years [i.e. present age] ,sons and father's age x+5 and 5x+5
After 2 years
3(x+5+2) = 5x+5+2
3x+15+6 = 5x+7
         14  =  2x
             x= 7 years
present age = x+5 = 12 and 5x+5 = 40
ratio = 40:12 = 20:6 = 10:3

2] The age of a father 10 years ago was thrice the son's age.10 years hence the fathers age will be twice that of his son.The ratio of their present ages is
a] 8:5 b]7:3 c]5:2 d]9:5

3] 1year ago a father was four times as old as his son.In 6 years timehis age exceeds twice his son's age by 9 years.Ratio present ages is
a] 13:4 b]12:5 c]11:3 d]9:2

4] 1year ago pramila was four times as old as her daughter.In 6 years time pramila's age exceeds her daughter's age by 9 years.Ratio present ages is
a] 13:4 b]12:5 c]11:3 d]9:2

1] The speed of the boat in still water is 10 kmph.If it can travel 24 km down stream and 14 km in the upstream in the equal time,indicate the speed of the flow of the stream.
a]38/100  b]100/38 c ]100+38  d] 100-38

solution:
let speed of flow of water = x
speed of boat downstream =  10+x
speed of boat upstream =  10-x
speed = distance travelled/time => d= st
distance downstream = 24 km
 distance travelled downstream= 24/(10+x)
distance upstream = 14
distance travelled upstream = 14/(10-x)
 since its given that distance covered upstream and down stream is in equal time
 24/(10+x) = 14/(10-x)
240-24x = 140x + 14x
x = 100/38

2] The speed of the boat in still water is 10 kmph.If it can travel 26 km down stream and 14 km in the upstream in th same time,indicate the speed of the flow of the stream.
a]8 b]3 c ]10 d] 2

1]If a:b = 5:9 and b:c = 4:7,find a:b:c
a] 20,30,60 b]20,36,60 c]20,30,63 d]20,36,63

a:b = 5:9
b:c = 4:7
b:c = [4* (9/4)] : [ 7*(9/4)]
      = 9: (63/4)
a:b:c = 5:9: (63/4) = 20: 36: 63

2]If a:b = 5:7 and b:c = 6:11,find a:b:c
a] 20,42,60 b]20,36,77 c]20,30,63 d]30,42,77

3]If a:b = 4:6 and b:c = 8:10,find a:b:c
a] 12,30,60 b]12,36,60 c]8,30,63 d]8,12,15

4]If a:b = 3:5 and b:c = 4:7,find a:b:c
a] 20,35,60 b]12,36,60 c]20,35,63 d]12,20,35

1] Three numbers are in the ratio 1:2:3 and their HCF is 12.The numbers are
a]12,24,36  b]12,26,36 c] 12,24,38 d] 14,24,36

let the required numbers be x,2x and 3x
the HCF is 12
so x= 12
the numbers are x = 12 , 2x = 24, 3x = 36

1] Two numbers are in the ratio of 15: 11.If their HCF is 13,find the number
a]190,140  b]191,141  c]192,143  d]195,143

let the required numbers be 15x and 11x
Then HCF is x
So x= 13
The numbers are 15*13 = 195 and 11*13 = 143

2] Two whole numbers are in the ratio of 15: 11.If their HCF is 7,find the number
a]100,77  b]105,141  c]105,77  d]195,143

2] A boat can be rowed 9 km upstream or 18 km downstream in a period of 3 hours.What is the speed of the boat in still water.
a] 2.5 kmph  b] 4.5 kmph  c] 6 kmph d] 8 kmph

solution
rate downstream = (9/3) = 3 kmph
rate upstream = (18/3) = 6 kmph
speed in still water = (1/2) (3+6) = 4.5 kmph

1] A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream,it takes 4 hours.What is the speed of the boat in still water.
a] 2  b] 4  c] 6 d] 8

solution
rate downstream = (16/2) = 8 kmph
rate upstream = (16/4) = 4 kmph
speed in still water is (1/2) (8+4) = 6 kmph

1] A man rows upstream 16 km and downstream 28 km taking 5 hours each time. the velocity of the current is
a] 2.4 km/hr  b] 1.2 km/hr  c] 3.6 km/hr  d] 1.8 km/hr

solution
 speed upstream = (16/5) = 3.2 km/hr
 speed downstream = (28/5) = 5.6 km/hr
velocity of current = (1/2)(3.2~ 5.6) = 1.2 km/hr


2] A man rows upstream 30 km and downstream 18 km taking 5 hours each time. What is the velocity of the current?
a] 2.4 km/hr  b] 1.2 km/hr  c] 3.6 km/hr  d] 1.8 km/hr

3] A man rows upstream 12 km and downstream 37 km taking 5 hours each time. What is the velocity of the current?
a] 4.5 km/hr  b] 2.5 km/hr  c] 3 km/hr  d] 4 km/hr