A Learning Portal from Recruitment India

A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water is added to the mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture.

A.

10 Liters

B.

12 Liters

C.

13 Liters

D.

20 Liters

Answer with explanation

Answer: Option AExplanation

Let the quantity of alcohol and water be 4x liters and 3x liters respectively.

Then,

(4x)/(3x+5) = 4/5

=> 20x = 4(3x+5)

=> x = 2.5

Quantity of alcohol = (4 * 2.5) liters = 10 liters.

Workspace

** A sum of Rs. 53 is divided among A, B, C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their shares is :**

A.

25:18:10

B.

24:10:15

C.

30:25:10

D.

25:12:18

Answer with explanation

Answer: Option AExplanation

Suppose C gets Rs. x. Then, B gets Rs.(x+8) and A gets Rs.(x+15).

Then, x+(x+8) +(x+15) = 53 ↔ x=10.

∴ A : B : C = (10+15): (10+8):10=25:18:10.

Workspace

If a 60 ml of water contains 12% of chlorine, how much water must be added in order to create a 8% chlorine solution?

A.

40ml of water

B.

50ml of water

C.

30ml of water

D.

35ml of water

Answer with explanation

Answer: Option CExplanation

Let x ml of chlorine be present in water.

Then, 12/100 = x/60 → x = 7.2 ml

Therefore, 7.2 ml is present in 60 ml of water.

In order for this 7.2 ml to constitute 8% of the solution, we need to add extra water. Let this be y ml.

Then, 8/100 = 7.2/y → y = 90 ml.

So in order to get an 8% chlorine solution, we need to add 90-60 = 30 ml of water.

Workspace

Find the third proportional between 16 and 20.

A.

24

B.

25

C.

28

D.

30

Answer with explanation

Answer: Option BExplanation

Let the third proportional of 16 and 20 be x.

Then 16, 20, x are in proportion.

This means 16 : 20 = 20 : x

So, 16 × x = 20 × 20

x = (20 × 20)/16 = 25

Therefore, the third proportional of 16 and 20 is 25.

Workspace

A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?

A.

12

B.

15

C.

18

D.

20

Answer with explanation

Answer: Option CExplanation

A:B = 2:3

B:C = 2:5

A:B:C = 4:6:15

6/25 * 75 = 18

Workspace

Pencils, Pens and Exercise books in a shop are in the ratio of 10: 2 : 3. If there are 120 pencils, the number of exercise books in the shop is:

A.

25

B.

27

C.

30

D.

36

Answer with explanation

Answer: Option DExplanation

Let Pencils = 10x, Pens = 2x & Exercise books = 3x.

Now,

10x = 120 hence x = 12.

Number of exercise books = 3x = 36.

Workspace

The speed of a bus increases by 22 kmph after every one hour. If the distance travelled in the first one hour was 3535 km, what was the total distance travelled in 1212 hours?

A.

422 km

B.

552 km

C.

502 km

D.

492 km

Answer with explanation

Answer: Option BExplanation

Workspace

If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?

A.

80 km

B.

70 km

C.

60 km

D.

50 km

Answer with explanation

Answer: Option DExplanation

He travels 2020 km more due to an increase of speed of 44 km/hr. Hence, with 1010 km/hr, he travels 20/4×10=50 km.

Workspace

A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?

A.

3

B.

4

C.

5

D.

6

Answer with explanation

Answer: Option DExplanation

Workspace

A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

A.

121 km

B.

242 km

C.

224 km

D.

112 km

Answer with explanation

Answer: Option CExplanation

Workspace

Three cats are roaming in a zoo n such a way that when cat A takes 5 steps, B takes 6 steps and C takes 7 steps.But the 6 steps of A are equal to the 7 steps of B and 8 steps of C. what is the ratio of their speeds?

A.

140:144:147

B.

40:44:47

C.

15:21:28

D.

252:245:240

Answer with explanation

Answer: Option AExplanation

Frequency of step of A:B:C = 5 : 6 : 7

But in terms of size of step, 6A = 7B = 8C

Therefore, Ratio of speeds of A, B and C = 5/6 : 6/7 : 7/8 = 140 : 144 : 147

Workspace

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

A.

8 : 9

B.

17 : 18

C.

21 : 22

D.

Cannot be determined

Answer with explanation

Answer: Option CExplanation

Workspace

Vipin can walk a certain distance in 52 days when he rests 10hours a day.how long will he take for twice the distance if he walks twice as fast as and rest twice as long each day

A.

75

B.

100

C.

182

D.

150

Answer with explanation

Answer: Option CExplanation

Vipin rests for 10 hours a day. As there are 24 hours in a day, the time he walks is 24 – 10 = 14 hours.

Total time taken = 52days X 14 = 728 hours

As distance is directly proportional to time, to cover double the distance he needs double the time.

That is, 2 x 728 hours.

But, as speed is inversely proportional to time and directly proportional to distance, double distance will require double speed.

That is, total time is

2/2 x 728 = 728 hours.

In the new situation, he rests for twice as much that is,

10 x 2 = 20 hours. Therefore he only walks for 24 – 20 = 4 hours.

If the number of days required is x,

4x = 728

x = 728/4

= 182 days

Workspace

One year ago a father was four times as old as his son .after 6 year his age exceed than twice of his son age by 9 year. Ratio of their present age is what

A.

30 yrs.

B.

33 yrs.

C.

20 yrs

D.

11 yrs

Answer with explanation

Answer: Option BExplanation

Lets denote the ages of the man and his son as M and S respectively.

One year ago their ages were M – 1 and S – 1 respectively.

So from the first statement, M – 1 = 4 * (S – 1) or

M – 4*S = -3 ← Equation 1

In 6 years time both would be older by 6 years, or M+6 and S+6.

From the second statement,

M + 6 = 2 * (S +6) + 9, or

M – 2*S = 15 ← Equation 2

Subtracting Equation 1 from Equation 2, we get:

M – 2*S – (M – 4*S) = 15 – (-3)

That is, 2*S = 18 , or S = 9. Therefore the Son’s present age is 9.

From Equation 2, M = 15 + 2*S or M = 15 + 18 = 33.

Therefore the Father’s present age is 33.

Workspace

An alloy of copper and tin weighing 1kg consist of 70% copper, how much copper should be added to it so that it would contain 75% copper? What will be the weight of the new alloy?

A.

30

B.

200

C.

90

D.

120

Answer with explanation

Answer: Option BExplanation

Suppose that x kg copper is to be added to the 1 kg alloy.

Now, we know that, the 1 kg alloy has 0.7 kg copper.

And, final percentage of copper in alloy is 75%.

(0.7+x)/(1+x)=75/100=3/4(0.7+x)/(1+x)=75/100=3/4

On cross-multiplication,

2.8+4x = 3+3x

x= 0.2

Therefore,

**0.2 kg or 200 g copper should be added to make it’s percentage in the alloy 75%**.

Workspace

The ratio of the number of boys to the number of girls in a class is 4:5. If there are a total of 54 students in the class, then what is the number of boys in the class?

A.

32

B.

40

C.

36

D.

24

Answer with explanation

Answer: Option DExplanation

Ratio of boys is to girl = 4:5.

Total number of boys = 4x

Total number or girls = 5x

Total number of students : 4x+5x= 9x

9x= 54, x=6.

Total number of boys = 4x = 4×6=24.

Workspace

If a carton containing dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors?

A.

2: 1

B.

3: 1

C.

3: 2

D.

1: 1

Answer with explanation

Answer: Option CExplanation

It is 3:2 I feel because on adding all the ratios only 3:2 results in 5 i.e 3+2=5 and 5 is not a factor of 12

Or

Here your first option is 2:1

Now splitting 12 in the Ratio 2:1 we get 8 and 4. So, it is possible.

Next you have 3:1 this is also possible ratio as it can be 9 and 3.

Now if we look at 3:2 then it is obviously not possible to split 12 into ratio of 3 and 2.

But still for last one we have7:5 this makes a total of 12. So 7 broken and 5 unbroken is also possible.

So, the correct answer is 3:2.

Workspace

The incomes of A,B and C are in a ratio of 7:9:12 and the expenditures are in a ratio of 8:9:15. If A saves 1/4 of its income then what will be the saving ratio of A ,B and C?

A.

56: 99: 69

B.

99: 56: 69

C.

56:99:69

D.

49: 69: 56

Answer with explanation

Answer: Option CExplanation

if u assume x and y and solving u will be annoyed.

Provided 1/4 is the saving, 3/4 is the expenditure

so Expenditure=3, Income = 4

first make A’s Income and Expenditure ratio parts as below

A

7*8 9*7 12*7

8*7 9*7 15*7

Now make first one as 4 parts by multiplying 4 and second make 3 parts by multiplying 3

A’s Income = 7*8*4 = 224

A’s Expenditure = 8*7*3=168 Saving = 56

Now

B’s Income = 9*8*4 = 288

B’s Expenditure = 9*7*3=189 Saving = 99

A’s Income = 12*8*4 = 384

B’s Expenditure = 15*7*3=315 so Saving = 69

Ratio 56:99:69.

Workspace

A cone hemisphere and a cylinder stand on the same base and have equal height find the ratio of their curved surface area

A.

l: h: r

B.

l:2h:r

C.

l:2h:2r

D.

2l:2h:2r

Answer with explanation

Answer: Option CExplanation

Given,

cone,hemisphere and cylinder have same base and equal height.

curved surface area of cone=πrl

curved surface area of cylinder=2πrh

curved surface area of hemisphere=2πr²

ratio=CSA of cone: CSA of hemisphere:CSA of cylinder

=πrl:2πrh:2πr²

=l:2h:2r

Workspace

5 apples and 4 pears cost as much as 7 pears and 3 apples. find out the ratio of the cost of one apple to the cost of one pear.

A.

3 : 2

B.

3 : 4

C.

3 : 1

D.

4 : 3

Answer with explanation

Answer: Option AExplanation

Given cost of 5 apples and 4 pears = cost of 7 pears and 3 apples

5A + 4P = 7P + 3A

2A=3P

A/P = 3/2

A:P = 3:2

Hence ratio of cost of 1 apple to 1 pear = 3 : 2

Workspace

Two number 3:4 ratio then sum of the square is625 find the number

A.

6, 8

B.

15, 20

C.

18, 24

D.

20, 25

Answer with explanation

Answer: Option BExplanation

Let the numbers be 3x, 4x

Given, their sum of their squares is 625

→ 9x²+16x²=625

25x²=625

x²=25

x=±5

So, the two numbers are ±15,±20

Workspace

The ages of raju amd biju are in the ratio 3:1 fifteen years hence,the ratio will be 2:1 their present ages are

A.

10

B.

15

C.

21

D.

20

Answer with explanation

Answer: Option BExplanation

The ratio of ages ,

=> 3:1

Let the age of raju be 3x .

And age of biju be x.

From the question,

=> x=15.

So, The age of raju is 3×15 =45years.

The age of biju=> 15.

Workspace

In a school, 10% of the boys are same in number as (1/4)th of the girls. what is the ratio of boys to girls in the school?

A.

3 : 2

B.

5 : 2

C.

2 : 1

D.

4 : 3

Answer with explanation

Answer: Option BExplanation

Let the number of boys in school be b

Let the number of girls in school be g.

Therefore , According to Question , 10% of boys is equal to 1/4 of girls→

10b/100 = 1g/4

or, 4×10b = 100×g

or, 40b = 100g

or, b/g = 100/40

or, b:g = 5:2

Workspace

If 2A = 3B = 4C, find A : B : C

A.

6 : 5: 3

B.

2 : 4 : 3

C.

6 : 4 : 8

D.

6 : 4 : 3

Answer with explanation

Answer: Option DExplanation

Let 2A = 3B = 4C = x

So, A = x/2 B = x/3 C = x/4

The L.C.M of 2, 3 and 4 is 12

Therefore, A : B : C = x/2 × 12 : x/3 × 12 : x/4 = 12

= 6x : 4x : 3x

= 6 : 4 : 3

Therefore, A : B : C = 6 : 4 : 3

Workspace

Divide $370 into three parts such that second part is 1/4 of the third part and the ratio between the first and the third part is 3 : 5. Find each part.

A.

500

B.

700

C.

400

D.

200

Answer with explanation

Answer: Option DExplanation

Let the first and the third parts be 3x and 5x.

Second part = 1/4 of third part.

= (1/4) × 5x

= 5x/4

Therefore, 3x + (5x/4) + 5x = 370

(12x + 5x + 20x)/4 = 370

37x/4 = 370

x = (370 × 4)/37

x = 10 × 4

x = 40

Therefore, first part = 3x

= 3 × 40

= $120

Second part = 5x/4

= 5 × 40/4

= $50

Third part = 5x

= 5 × 40

= $ 200

Workspace

Find the third proportional of 16 and 20.

A.

25

B.

28

C.

27

D.

25

Answer with explanation

Answer: Option DExplanation

Let the third proportional of 16 and 20 be x.

Then 16, 20, x are in proportion.

This means 16 : 20 = 20 : x

So, 16 × x = 20 × 20

x = (20 × 20)/16 = 25

Therefore, the third proportional of 16 and 20 is 25.

Workspace

A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be :

A.

9 : 5

B.

7 : 5

C.

5 : 9

D.

5 : 7

Answer with explanation

Answer: Option BExplanation

Workspace

Correct Answer 👍

Wrong Answer 👎