### Find solutions for all the questions at the end of each set:

### Set A

1. In a shower, 5 cm of rain falls. The volume of water that falls on 2 hectares of ground, is

(a) 100 m^3

(b) 1000 m^3

(c) 10000 m^3

(d) 10 m^3

2. The LCM of two prime numbers x and y (x>y) is 161. The value (3y-x) is

(a) -2

(b) -1

(c) 1

(d) 2

3. A is thrice as good as a workman B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in

(a) 20 days

(b) 221/2 days

(c) 25 days

(d) 30 days

4. 94 is divided into two parts in such a way that fifth part of the first and eighth part of the second are in the ratio 3 :4. The first part is

(a) 27

(b) 30

(c) 36

(d) 48

5. Of the three numbers, the ratio of the first and the second is 8 : 9 and that of the second and third is 3 : 4. If the product of the first and third number is 2400, then the second number is

(a) 45

(b) 40

(c) 30

(d) 35

6. In what ratio must a grocer mix teas worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

(a) 3 : 2

(b) 3 : 4

(c) 3 : 5

(d) 4 : 5

7. A boat is rowed downstream at 15.5 km/h and upstream at 8.5 km/h the speed of the stream is

(a) 3.5 km/h

(b) 5.75 km/h

(c) 6.5 km/h

(d) 7 km/h

8. A sum of money amounts to Rs. 6690 after 3 yr and to Rs. 10035 after 6 yr on compound interest. The sum is

(a) Rs. 4000

(b) Rs. 4445

(c) Rs. 4460

(d) Rs. 4520

9. If p=999, then the value of ∛(p(p^2+3p+3)+1) is

(a) 1000

(b) 999

(c) 998

(d) 1002

10. If (x+1)/x=3, then the value of (x^5+1)/x^5 is

(a) 123

(b) 126

(c) 113

(d) 129

Answer Key:

1.b

2.a

3.b

4.b

5.a

6.a

7.a

8.c

9.a

10.a

### Find solutions for all the questions at the end of each set:

### Set B

1. The ratio of age of A and B is x:y. If A’s age is increased by 3 years and B’s age is increased 2 years then new ratio of their ages becomes 24:25.Given that the sum of their actual ages is 93 years. Find the actual ratio of their ages.

(a) 21 : 22

(b) 42 : 45

(c) 45 : 48

(d) can’t be determined

2. a : b = 4 : 9 if 4 is added to both of the numbers then the new ratio becomes 21 : 46. What is the difference between a and b?

(a) 80

(b) 100

(c) 125

(d) 130

3. 6 pumps of kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same tank in 18 days. What is the ratio of the efficiency of a Kirlosker pump and a USHA pump?

(a) 6 : 7

(b) 7 : 6

(c) 7 : 54

(d) can’t be determined

4. 16 person can reap 1/5th field in 6 days. How many person (with same efficiency) are required to reap rest of the field in 8 days?

(a) 27

(b) 54

(c) 48

(d) 64

5. Pertrol is 7 times heavy than Kerosene and Castrol mobil is 18 times as heavy as Kerosene. What should be the ratio of petrol and mobil in the new mixture to get the mixture which must be 11 times as heavy as kerosene?

(a) 3 : 4

(b) 7 : 4

(c) 9 : 19

(d) 9 : 10

6. A girl buys 2 pigeons for Rs. 182. She sells one at a loss of 5% and another at a profit if 8%. But she neither gains nor loses on the whole. Find the price of pigeon which has sold at a profit:

(a) Rs. 112

(b) Rs. 85

(c) Rs. 70

(d) can’t be determined

7. The ratio of price of Cello and Parker pens in 2000 were in the ratio of 3 : 5. In 2005 the price of Cello pen trebles itself and the price of Parker pen is increased by Rs. 100, then the new ratio of prices of the same pens becomes 4 :5. What was the original price of the Parker pen in 2000?

(a) Rs. 60

(b) Rs. 80

(c) Rs. 100

(d) Rs. 120

8. A goldsmith has 361 rings of gold. He sells some of them at a loss of 4% and rest at a profit of 15% marking overall profit of 8%. Find the no. of rings sold at a profit of 15%:

(a) 171

(b) 133

(c) 218

(d) 228

9. Michel travelled from New York to New Jersey covering total distance of 250 miles in 8 hr. partly by car at 30 miles/hr. and rest by train at 35 miles/hr. The distance travelled by car is:

(a) 150 miles

(b) 80 miles

(c) 220 miles

(d) 180 miles

10. A rabit takes 22 leaps for every 17 leaps of cat and 22 leaps of a rabit are equal to 17 leaps of the cat. What is the ratio of the speeds of rabit and cat?

(a) 1 : 1

(b) 484 : 289

(c) 17 : 22

(d) none of these

Solution

1. x+y=93 ……………(i)

And (X+3)/(y+2)=24/25

25x-24y=(-27) ……….(ii)

From equation number (i) and (ii)

x=45 and y=48

2. a/b=4x/9x and (a+4)/(b+4)=21/46

a=80 and b=180

∴b-a=100

3. The number of days required by a single Kirlosker pumps to fill the tank=6×7=42 days and the number of days required by a single USHA pump to fill the same tanks=2×18=36 days.

Now, since efficiency is inversely proportional to the number of days. Hence,

(Efficiency of on K-pump)/(Efficiency of U-pump)=36/42=6/7

4. 1/5th field can be reaped by 96 man days

∴4/5th field can be reaped by 96×4=384 man days

Now, since there are only 8 days so required number od men=384/8=48 men

5. If the weight of kerosene be k kg/unit volume, then

Weight of petrol= 7 k/unit volume

Weight of Castrol=18 k/unit volume

Required weight of the mixture=11 k/unit volume

By Allegation

The required ratio is 7 : 4.

6. By Allegation

The ratio of price of pigeons sold at loss and profit respectively are in the ratio of 8 : 5

∴ Cost price of profitable pigeon=5/(8+5)×182=Rs.70.

7. C/R=3x/5x

Again C/R=(3x)3/(5x+100)=4/5

x=16

∴ Price PARKER pen in 2000 was Rs. 80.

8. By Allegation

Now, we get the ratio of no. rings sold at a loss and profit is 7 : 12

∴ Number of rings sold at profit=12/19×361=228

Alternatively: Go through options.

9. Best way is to go through option consider option (d)

180/30+70/35=6+2=8 hrs

Hence, (d) is correct.

Alternatively: x/30+(250-x)/35=8

x=180 miles

Alternatively: Since the Average Speed=(Total Distance)/(Total time)=250/8 miles/hr

∴ By Allegation

Therefore, the ratio of time taken @ 30 m/hr and @ 35 m/hr is in the ratio of 3 : 1. It means he has travlled @ 30 m/hr for 6 hr.

Therefore, the distance travelled by car is 180.

(∵ Distance=Speed×Time).

10.22/22:17/17=1∶1

### Find solutions for all the questions at the end of each set:

### Set C

1. x is a five-digit number. The digit in ten thousand’s place is 1. The number formed by its digit in unit’s and ten’s places is divisible by 4. The sum of all the digits is divisible by 3. If 5 and 7 also divide x, then x will be

(a) 14040

(b) 12060

(c) 10020

(d) 10080

2. What is the weight of a cubical block of ice 50 cm in length, if one cubic metre of ice weights 900 kilograms?

(a) 113 kg

(b) 113.5 kg

(c) 112.5 kg

(d) 114 kg

3. If A, B and C are three numbers, such that, the LCM of A and B is B and the LCM of B and C is C, then the LCM of A, B and C is

(a) A

(b) B

(c) C

(D) (A+B+C)/3

4. In a class of 64 students, 50% of the students have taken Sociology and 75% of the students have taken Political Science. All Students have chosen either one subject. How many students have taken both the subjects?

(a) 12

(b) 18

(c) 14

(d) 16

5. Six men earn as much as seven women, two women earn as much as three boys, four boys earn as much as five girls. If a girl earns Rs.16 a week, what does a man earn per week?

(a) Rs.35

(b) Rs.20

(c) Rs.40

(d) Rs.30

6. Find the arithmetic mean of 8 no.between 1 and 10.

(a) 2.5

(b) 5.5

(c) 3.5

(d) 4.5

7. In an examination, A obtain 10% less than the minimum number of marks required for passing, B obtains 11(1/9) less than A, and C obtains 41(3/17)% less than the number of marks obtained by A and B together. Does C pass or fail?

(a) Pass

(b) Fail

(c) Can’t say

(d) Data inadequate

8. The marked price of a shirt and a trouser are in the ratio 2 : 3. The shopkeeper gives 30% discount on the shirt. If the total discount is 20%. Then, the discount offered on the trouser is –

(a) 12(1/2)%

(b) 33(1/3)%

(c) 13(1/3)%

(d) 8(1/3)%

9. A, B and C are partners in a business. A, whose money has been used for 4 months, claims 1/8 of the profit. B, whose money has been used for 6 months, claims 1/3 of the profit. C had invested Rs. 1560 for 8 months. How much money did A and B contribute together?

(a) 720

(b) 1560

(c) 2000

(d) 1280

10. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. Then my age and my son’s age are respectively:-

(a) 42 yrs, 14 yrs

(b) 45 yrs, 15 yrs

(c)36 yrs, 12 yrs

(d) 48 yrs, 16 yrs

Answers.....

1. (d)

No number except 10080 is divisible by 7.

further,80 is divisible by 4.

1+0+0+8+0 = 9 is divisible by 3 and 10080 is also divisible by 5.

2. (c)

volume of the cubical block of ice = 50*50*50 cm^3

= (50*50*50)/(100*100*100) m^3 = 1/8 m^3

weight of the cube = 1/8*900 = 112.50 kg

3. (c)

LCM of A & B is B => B is a multiple of both A & B

Again,

LCM of B & C is C => C is a multiple of both B & C

so LCM of ABC = C

4.(d)

5. (a)

6 men = 7 women;

2 women = 3 boys;

4 boys = 5 girls;

Now earning of a girls per week = Rs. 16

so Earning of 1 boy = 5/4*16 = 20

Earning of 1 women = 3/2*20 = 30

Earning of 1 man = 7/6*30 = 35

6. (b)

8 arithmetic mean between 1 and 10

= 2,3,4,5,6,7,8,9

Their mean = (2+3+4+5+6+7+8+9)/8 = 5.5

7. (a)

8. (c)

9. (c)

Ratio of their profit= 1/8 : 1/3:(1-(1/8+1/3))

= 1/8 : 1/3 : 13/24

= 3:8:13

Now,for A & C

A*4 :c*8 = 3:13

A*4 :1560*8 = 3:13

A = (1560*8*3)/(4*13) = 720

For B & C,

B*6 :c*8 = 8:13

B*6 :1560*8 = 8:13

B = (1560*8*8)/(6*13) = 1280

Contribution by A & B together

= 720+1280= 2000

10. (b)

Let the present age of my son = x yrs.

Then,the present age of mine = 3x yrs.

(3x+5)=2(1/2)(x+5)

x = 15 yrs.

Father's age = 45 yrs.

Son's age = 15 yrs.

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