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__START QUIZ__Total distance between A to B is 240 km. Ram boards Train P & it starts running with an average speed of ‘X’ kmph from A to B, while on another train Q, Radha boards from A to reach B. Train Q starts running from B after 2 hours of train P and reaches A, 60 minutes before train P. If train P stops for 60 minutes at a line crossing and second train did not stop at any place, then the ratio between the average speed of train P to average speed of train Q is 4:5. After reaching B, Ram meets his two daughters Roly & Beauty & distributed Rs.17000 between them & thus Roly got Rs ‘R’ & Beauty got Rs ‘S’ and further both of them invested their amounts at the rate of (X-6) % SI per annum. The age of Beauty and Roly at that time was 18 months and ‘X’ months respectively and such that each daughter may get equal amounts, when they attain the age of 21 months. Roly, invests Rs ‘K’, which she received at the age of 21, & its value increases by ‘X’% every month. The difference between the price at the end of the third month and fourth month is ‘W’.

1.Find the difference between ‘S’ & ‘R’.

1920

2250

1725

2885

2025

2.Find the difference between ‘W’ & ‘K’.

11246

12556

10546

14566

None of these

3.A vessel is filled with liquid, ‘X’ parts of which is water and ‘R/295’ 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?

7/60

5/26

8/35

13/50

5/21

4.A box contains X white, R/295 red and S/875 blue erasers. If five erasers are taken at random then the probability that all the five are blue color is:

1/25925

7/25944

3/132

2/21345

None of these

5.Find the value in the place of ‘X’

12

12.5

13

13.5

14

6.5 bottles of water and 9 bottles of milk together fill 71 glasses. Also, 7 bottles of water and 11 bottles of milk together fill 93 glasses. How many glasses can be filled with 3 bottles of water and 4 bottles of milk if each bottle of either of the water or milk fills an integer number of glasses?

37

41

34

45

32

7.A reduction of 20% in the price of wheat enables a buyer to buy 1.25 kgs more for Rs. 275. Find the original and reduced prices per kg of wheat.

Rs 80, Rs 64

Rs 90, Rs 72

Rs 55, Rs 44

Rs 75, Rs 60

None of these

8.Length and Breadth of a rectangle are 14m. and 16m. and its area is equal to the length of a square. What will be the length of the diagonal of the square?

222

223

224

224v2

225

9.A mixture contains water and milk in the ratio of 3 : 5. If 4 litres of water and 5 litres of milk are added to the mixture, the ratio of water and milk becomes 2 : 3. What is the quantity of water in the final mixture?

11 litres

12 litres

8 litres

10 litres

9 litres

10.In a 200 m race, Rahul beats Amit by 40 meters. In the same race, Amit beats Prabhat by 30 metres. Now Rahul and Prabhat run a 500 m race. Assuming that their speeds are same as earlier than by how much distance will Rahul beat Prabhat?

210 m

175 m

150 m

160 m

140 m

11.A thief steals a car at 8 a.m and rides the bike at an average speed of 40 km/h. The theft was found at 9.30 a.m and the policeman started chasing on bike at a speed of 70kmph. When will he catch the thief?

10.30 a.m

11.30 a.m

12 noon

12.30 pm

He cannot catch him

12.The ratio of wine and water in the container is 4:3 when 15 liters of the mixture is taken out and is replaced by the water, the ratio become 3:4. Then total quantity of the mixture in the container is:

60

11

33

20

64

13.Rahul invested 60% of his interest from a S.I on Rs. 25,000 @ 12.5% for 2 years into a business for 6 months. Sumit invested an amount that was 20% of Rahul's interest in the same business for 5 months but withdrew 25% of it at the end of 3 months. If their profit in the business was Rs. 20,000, find Rahul’s share of profit-

Rs. 18,000

Rs. 16,000

Rs. 12,000

Rs. 8,000

Rs. 7,500

14.At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

2 (2/3) miles per hr

2 miles per hr

11/4 miles per hr

3 miles per hr

None of these

15.A man invests Rs. X in scheme ‘A’ and Rs 1.5X in scheme ‘B’ sheme ‘A’ offers 20% p.a. at S.I and scheme ‘B’ offers 10% p.a. at C.I. If total interest earned by him after 2 years is Rs. 572, then find the interest earned from scheme ‘B’ ?

Rs. 320

Rs. 252

Rs. 168

Rs. 430

Rs. 336

**QUANTITY COMPARISION**

16.Quantity I: A and B can do a piece of work individually in 16 days and 12 days respectively. A started the work. After how many days should B join so that the work is completed in 12 days?

Quantity II: P and Q can do a piece of work individually in 12 days and 8 days respectively. They work on alternate days starting with A. In how many days will the total work be completed?

17.Quantity I: A person walks at a speed of 6 km/hr. He takes a rest of 1 minute for every half km. In how much time he can travel a distance of 4 km

Quantity II: Train A leaves Hyderabad for Secunderabad at 04:30 am and reaches Secunderabad at 06:30 am. Train B leaves Secunderabad for Hyderabad at 05:30 am and reaches Hyderabad at 08:30 am. After how many minutes of B’s start they will meet?

18.Quantity I: The ratio of present ages of Mahesh and his father is 2 : 5. Father’s age at the time of Mahesh’s birth is 24 years. Find the sum of their present ages.

Quantity II: A father said to his son, “ I was as old as you are at present at the time of your birth. If the father’s present age is 28 years, find the sum of their present ages.

19.Quantity I: In a party, each person shakes hand with every other person. If there are total 45 handshakes, then the total number of persons present are?

Quantity II: In a party, each person shakes hand with every other person. If there are 8 persons, then the number of handshakes possible are?

20.Length of a rectangle is same as side of square whose are is 784 cm^2 while breadth of rectangle is same as side of another square whose perimeter is 88 cm. Find the area of rectangle?

616 cm2

624 cm2

336 cm2

396 cm2

1216 cm2

__SOLUTIONS:__

1.Rate % at which Roly & Beauty invested their amounts = (X-6) % =12-6 = 6 %

Now, Ratio of their amounts,

Roly : Beauty

:

59 : 77

Amount of Roly = 59/136×17000=7375 = R

Amount of Beauty =77/136×17000=9625=S

So, S-R = 9625-7375 = 2250

2.

3.

4.

5.ATQ,

Speed of train P = X, Speed of train Q =5X/4

Now let time taken by Train P to reach B = T hrs

So, X × (T+1) =5X/4 × (T-3)

T = 19 hrs

So, X × (T+1) = 240

S = 12

6.Let 1 bottle of water fill ‘a’ glasses and 1 bottle milk juice fill ‘m’ glasses.

We have 5a + 9m = 71 and 7a + 11m = 93.

Solving we get a = 7 and m = 4.

So 3 bottles of water and 4 bottles of milk will fill = 7*3 + 4*4 = 37 glasses

7.Let the original price per kg of wheat = x

Therefore reduced price = 0.8x

Quantity before price reduction = Total cost / cost per kg = 275/x

Quantity after price reduction = 275 / 0.8x

==> (275/x)+1.25 = (275/0.8x)

==> x = Rs 55.

==> 0.8x = Rs 44

8.Area of rectangle = 224 sq.m.

So side of square = 224

Diagonal of square= 224√2

9.Let the quantity of water and milk be 3x and 5x

It is given that, (3x+4)/(5x+5)=2/3

On solving, we get x = 2

Therefore, the quantity of water in the final mixture = (3 * 2 + 4) litres = 10 litres.

10.In the time that Rahul runs 200 m, Amit runs 160 m. Hence, the ratio of their speeds is 5:4. Now, in the time that Rahul runs 200 m, Amit runs 170 m. Hence, the ratio of their speeds is 20:17

Thus, we can say that the ratio of the speeds of all three people will be 25:20:17

Hence, the ratio of the speeds of Rahul and Amit is 25:17.

Hence, in the time that Rahul travels 500 m, Amit will travel 340 m. Thus, Rahul will beat Amit by 160 m.

11.Thief stealt the car at 8 a.m and rides at a speed of 40 km/h Theft was found at 9.30 a.m

In 1 hour 30 minutes, thief travels = 40 x 1 hour 30 minutes = 60 km.

So, thief was 60 km ahead of policeman.

At 9.30 policemen started chasing at a speed of 70 km/h.

As they both are moving in same direction, relative speed = 70-40 = 30 km/h

Time taken by policeman to cover 60 km travelled by thief already = 60 / 30= 2 hours.

Starting counting 2 hours from 9.30 am, thief will be caught at 11.30 am.

12.Let the total quantity of mixture be x

Initial ratio of wine and water= 4:3

Final ratio of mixture after replacement= 3:4

We know,

Remaining Quantity/Initial Quantity= (1 – replaced quantity/total quantity)

¾= 1- 15/x

15/x= 1-3/4

15/x= 1/4

x= 60 liters

13.Interest as S.I = (P x R x T)/100 = 25000 x 12.5 x 2 /100 = Rs.6250

He invests 60% of interest = 0.6 of 6250 = Rs.3750

Rahul invested Rs.3750 for 6 months

Sumit invested 20% of Rahul’s interest = 0.2 of 6250 = Rs.1250

Sumit invested Rs.1250 for 3 months, then

Taking out 25% of 1250 = Rs.312.5

Invested amount for remaining 2 months = 1250-312.5 = Rs.937.5

So, Rahul’s investment = 3750 x 6 = 22500

And, Sumit’s investment = (1250 x 3) + (937.5 x 2) = 3750+1875

= 5625

Ratio profits is ratio of investments.

Rahul’s profit / Sumit’s profit = 22500 / 5625 = 4/1

So, [Rahul’s profit ratio](total profit) = Rahul’s profit

Rahul’s profit = [4/(4+1)](20000) = 80000/5 = Rs.16,000

14.Let the speed of Rahul in still water be x mph

and the speed of the current be y mph

Then, Speed upstream = (x – y) mph

Speed downstream = (x + y) mph

Distance = 12 miles

Time taken to travel upstream – Time taken to travel downstream = 6 hours

12/(x-y) – 12/(x+y)=6

x2=y2+4y—1

Now he doubles his speed. i.e., his new speed = 2x

Now, Speed upstream = (2x – y) mph

Speed downstream = (2x + y) mph

In this case, Time taken to travel upstream – Time taken to travel downstream = 1 hour

12/(2x-y) – 12/(2x+y) = 1

4x2=y2+24y—2

From 1 and 2 we get

4y+y2=(24y +y2)/4

Y=8/3==> 2 2/3mph

15.Overall rate for 2 years in scheme ‘A’ =2×20=40%

Overall rate for 2 years in scheme ‘B’

= 10 +10 + (10×10)/100=21%

ATQ,

40X/100+(21×1.5X)/100=572

40X+31.5X=57200

⇒X=57200/71.5=800

Interest earned from scheme ‘B’

=1.5×800×21/100=252

16.Quantity I:

Let the total work be 48 units (LCM of 16 and 12)

Efficiency of A = 48/16 = 3 units/day

Efficiency of B = 48/12 = 4 units/day

Let us assume that B joins after ‘x’ days.

A works for x days and completes 3x units

Remaining work = 48-3x units

Total work needs to be completed in 12 days.

Then, 48-3x units needs to be completed by A and B in 12-x days.

⇒ (48-3x)/7 = 12-x

⇒ 48-3x = 84-7x

⇒ 4x = 36

⇒ x = 9

Therefore, B joins after 9 days.

Quantity II:

Let the total work be 24 units (LCM of 12 and 8)

Efficiency of P = 24/12 = 2 units/day

Efficiency of Q = 24/8 = 3 units/day

They work on alternate days starting with P.

Then, 5 units of work will be completed in 2 days.

⇒ 20 units of work will be completed in 8 days.

Remaining work = 24-20 = 4 units

2 units will be completed by P in next 1 day.

Remaining work = 4-2 = 2 units.

Q can complete 2 units of work in ⅔ days

Hence, Total work will be completed in 8+1+⅔ = 92/3+2/3 days

Therefore, Quantity I < Quantity II

17.Quantity I:

Speed of the person = 6 km per hour

⇒ He travels 1 km in 10 minutes

Time taken for him to travel 4 km = 40 minutes

Given that he takes 1 minute rest for every half km.

He travels 3 and half km by taking rest and after last half km, he reaches his destination.

Hence, Rest time for 0.5 km = 1 min

Rest time for 3.5 km = 7 min

Therefore, Total time taken = 40+7 = 47 minutes.

Quantity II:

Time taken for train A to travel from Hyderabad to Secunderabad = 2 hours.

Time taken for train B to travel from Secunderabad to Hyderabad = 3 hours.

Let the total distance between Hyderabad and Secunderabad = D km

Speed of train A = D/2 km/hr

Speed of train B = D/3 km/hr.

Distance travelled by train A in 1 hour(04:30 am to 05:30 am) = D/2×1=D/2 km

Remaining distance = D-D/2 = D/2 km

Hence, Time taken to meet = (D/2)/(D/2+(D )/3)= 3/5 hours = ⅗*60 = 36 minutes.

Therefore, Quantity I > Quantity II

18.Quantity I:

Let their present ages be 2x years and 5x years respectively.

Father’s age at the time of Mahesh’s birth will be 7x - 5x = 3x years.

Given, 3x = 24

⇒ x = 8

Hence, The sum of their present ages = 5x+2x = 7x years = 7*8 = 56 years.

Quantity II:

Let the present age of the son be x years.

Then, The father’s age at the time of son’s birth = 28 - x years

Given, 28 - x = x

⇒ 2x = 28

⇒ x = 14

Therefore, The sum of their present ages = 28+14 = 42 years.

Therefore, Quantity I > Quantity II.

19.Quantity I:

Number of handshakes possible = n(n-1)/2 where n = number of persons

Given,

⇒ n(n-1)/2=45

Solving,

n = 10 or n = -9

Number of persons cannot be negative.

Hence, Total number of persons is 10.

Quantity II:

Number of handshakes possible = n(n-1)/2 where n = number of persons.

= (8×7 )/2 = 28

Therefore, Quantity I < Quantity II

मात्रा I:

हाथों की संख्या संभव = n(n-1)/2जहाँ n = व्यक्तियों की संख्या

दिया गया, = n(n-1)/2=45

⇒ n = 10 या n = -9

20.Length of rectangle =√784=28

Breadth of rectangle =88/4=22

Area of rectangle =28×22=616 cm2

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