### Aptitude - Ratio And Proportion

What is the ratio of third proportional to 12 and 30 and the mean proportional between 9 and 25 is?

A.  5 : 1

B.  1 : 5

C.  5 : 2

D.  2 : 5

Correct Answer :

5 : 1

Explanation :

Say A : B = 12 : 30

First, we need to find third proportion

A : B = B : C => 12 : 30 = 30 : C

=> C = 75

Next, we need to find mean proportion of 9 and 25

So, Mean Proportion (D) = √ 9 x 25 = 15

We need to find C : D

=> 75 : 15 = 5 : 1

A bag contains 50p, 25p and 10p coins in the ratio 5 : 9 : 4 amounting to Rs.206. Find the number of coins of 10p?

A.  206

B.  200

C.  360

D.  160

Correct Answer :

160

Explanation :

Given that, Total amount = Rs.206/-

50p : 20p : 10p = 5 : 9 : 4

As total amount is in rupees convert the paise into rupees.

Say Z is the ratio constant

=> 5Z x 0.5 + 9Z x 0.25 + 4Z x 0.1 = 206

=> Z = 40

The number of 10p coins = 4Z = 4 x 40 = 160

In a class, there are 100 students and among them 40 are girls. What is the ratio of the number of boys to the number of girls?

A.  3 : 2

B.  2 : 3

C.  1 : 1

D.  3 : 4

Correct Answer :

3 : 2

Explanation :

Given that, Total students = 100

Girls = 40

=> Boys = 100 - 40 = 60

Ratio of number of boys to number of girls is

=> 60 : 40 = 3 : 2

The Ratio of Science and Arts students in a college is 4:3. If 14 Science students shift to Arts then the ratio becomes 1:1. Find the total strength of students in both science and arts together

A.  196

B.  206

C.  296

D.  306

Correct Answer :

196

Explanation :

Ratio of Science and Arts  students = 4:3

Say, the ratio constant is Z, so that the ratio = 4Z:3Z

Given, 14 Science students shifted to Arts

=> (4Z - 14) : (3Z + 14) = 1 :1

=> Z = 28

Total Students = 4Z + 3Z = 196

If 0.75 : Z : : 5 : 8, then Z is equal to

A.  1.1

B.  1.2

C.  1.3

D.  1.4

Correct Answer :

1.2

Explanation :

Given that 0.75 : Z : : 5 : 8

=> Z x 5 = 0.75 x 8

=> Z = 6/5

=> Z = 1.2

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

A.  2 : 5

B.  3 : 5

C.  4 : 5

D.  7 : 5

Correct Answer :

4 : 5

Explanation :

Let the third number be z

First number  =  120% of z = 120z/100 = 6z/5

Second number = 150% of z = 150z/100 = 3z/2

Ratio of these two numbers = 6z/5 : 3z/2 = 12z : 15z = 4 : 5

A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?

A.  Rs. 460

B.  Rs. 484

C.  Rs. 550

D.  Rs. 664

Correct Answer :

Rs. 484

Explanation :

(4/15) A = (2/5) B

=> A = [ (2/5) x (15/4) ] B

=> A = (3/2) B

=> A/B = 3/2

=> A : B = 3 : 2

=> B's share = Rs. [ 1210 x (2/5) ] = Rs. 484

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

A.  Rs. 500

B.  Rs. 1000

C.  Rs. 1500

D.  Rs. 2000

Correct Answer :

Rs. 2000

Explanation :

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively

Then, 4x - 3x = 1000

=> x = 1000

=> B's share = Rs. 2x = (2 X 1000) = Rs. 2000

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

A.  2 : 3 : 4

B.  6 : 7 : 8

C.  6 : 8 : 9

D.  None of these

Correct Answer :

2 : 3 : 4

Explanation :

Originally, let the number of seats for Mathematics, Physics and Biology be 5z, 7z and 8z respectively

Number of increased seats are (140% of 5z), (150% of 7z) and (175% of 8z)

=> [ (140/100) x (5z) ] , [ (150/100) x (7z) ] and [ (175/100) x (8z) ]

=> 7z, (21z/2) and 14z

=> The required ratio = 7z : (21z/2) : 14z

=> 2 : 3 : 4

In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

A.  20 litres

B.  40 litres

C.  60 litres

D.  80 litres

Correct Answer :

60 litres

Explanation :

Quantity of milk = 60 x (2/3) litres = 40 litres

Quantity of water in it = (60-40) litres = 20 litres

New ratio = 1 : 2

Let quantity of water to be added further be z litres

Then, milk : water = 40/(20+z)

Now, 40/(20+z) = 1/2

=> 20+z = 80

=> z = 60

=> Quantity of water to be added = 60 litres

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

Correct Answer :

21 : 22

Explanation :

Originally, let the number of boys and girls in the college be 7z and 8z respectively.

Their increased number is (120% of 7z) and (110% of 8z)

=> [ (120/100) x 7z ] and [ (110/100) x 8z ]

=> 42z/5 and 44z/5

=> The required ratio = ( 42z/5 : 44z/5 ) = 21 : 22

Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

A.  Rs. 17,000

B.  Rs. 20,000

C.  Rs. 25,500

D.  Rs. 38,000

Correct Answer :

Rs. 38,000

Explanation :

Let the original salaries of Ravi and Sumit be Rs. 2z and Rs. 3z respectively

Then, (2z+4000) / (3z+4000) = 40 / 57

57(2z + 4000) = 40(3z + 4000)

6z = 68,000

3z = 34,000

Sumit's present salary = (3z + 4000) = Rs.(34000 + 4000) = Rs. 38,000

The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

A.  20

B.  30

C.  40

D.  50

Correct Answer :

30

Explanation :

Let the three parts be A, B, C.

Then, A : B = 2 : 3 and B : C = 5 : 8 = (5 x (3/5)) : (8 x (3/5)) = 3 : 24/5

=> A : B : C = 2 : 3 : 24/5 = 10 : 15 : 24

=> B = 98 x (15/49) = 30

If Rs. 782 be divided into three parts, proportional to 1/2 : 2/3 : 3/4 then the first part is:

A.  Rs. 182

B.  Rs. 190

C.  Rs. 196

D.  Rs. 204

Correct Answer :

Rs. 204

Explanation :

Given ratio =1/2 : 2/3 : 3/4 = 6 : 8 : 9

=> 1st part = Rs. ( 782 x (6/23) ) = Rs. 204

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A.  3 : 3 : 10

B.  10 : 11 : 20

C.  23 : 33 : 60

D.  Cannot be determined

Correct Answer :

23 : 33 : 60

Explanation :

Let A = 2k, B = 3k and C = 5k

A's new salary = (115/100) x 2k = 23k/10

B's new salary = (110/100) x 3k = 33k/10

C's new salary = (120/100) x 5k = 6k

=> New Ratio = [ (23k/10) : (33k/10) : 6k ] = 23 : 33 : 60

If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

A.  2 : 5

B.  3 : 7

C.  5 : 3

D.  7 : 3

Correct Answer :

5 : 3

Explanation :

Let 40% of A = (2/3) B

Then, (40A/100) = (2B/3)

=> 2A/5 = 2B/3

=> A/B = [ (2/3) x (5/2) ] = 5/3

=> A : B = 5 : 3

The fourth proportional to 5, 8, 15 is:

A.  16

B.  20

C.  24

D.  28

Correct Answer :

24

Explanation :

Let the fourth proportional to 5, 8, 15 be z

Then, 5 : 8 : 15 : z

=> 5z = (8 x 15)

=> z = 24

Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

A.  27

B.  30

C.  33

D.  36

Correct Answer :

33

Explanation :

Let the numbers be 3z and 5z

Then, (3z-9) / (5z-9) = 12 / 23

=> 23 (3z-9) = 12 (5z-9)

=> z = 11

=> The smaller number = (3 x 11) = 33

In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

A.  50

B.  100

C.  150

D.  200

Correct Answer :

150

Explanation :

Let the number of 25 p, 10 p and 5 p coins be z, 2z and 3z respectively

Then, sum of their values = Rs. [ (25z/100) + ((10x2z)/100) + ((5x3z)/100) ] = Rs. (60z/100)

=> (60z/100) = 30

=> z = 50

Hence, the number of 5 p coins = (3 x 50) = 150

Which of the following fractions is the smallest?

A.  13/16

B.  15/19

C.  17/21

D.  7/8

Correct Answer :

15/19

Explanation :
No Explanation available for this question

If A : B =8 : 15, B : C = 5 : 8 and C : D = 4 : 5, then A : D is equal to:

A.  2 : 7

B.  4 : 15

C.  8 : 15

D.  15 : 4

Correct Answer :

4 : 15

Explanation :
No Explanation available for this question

Hitesh is 40 years old and Ronnie is 60 years old. How many years ago was the ratio of their ages 3 : 5 ?

A.  5 years

B.  10 years

C.  20 years

D.  37 years

Correct Answer :

10 years

Explanation :
No Explanation available for this question

Girish started a business investing Rs. 45,000. After 3 months, Vijay joined him with a capital of Rs. 60,000. After another 6 months, Ankush joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. What is Girish’s share of profit ?

A.  Rs. 5,500

B.  Rs. 6,000

C.  Rs. 6,600

D.  As. 5,900

E.  None of these

Correct Answer :

Rs. 5,500

Explanation :
No Explanation available for this question

If a/3 = b/4 = c/7, then a + b + c /c is equal to:

A.  7

B.  2

C.  1/2

D.  1/7

Correct Answer :

2

Explanation :
No Explanation available for this question

Two whole numbers whose sum is 72 cannot be in the ratio:

A.  5 : 7

B.  3 : 5

C.  3 : 4

D.  4 : 5

Correct Answer :

3 : 4

Explanation :
No Explanation available for this question

If 15% of x = 20% of y, then x : y is:

A.  3 :4

B.  4 : 3

C.  17 :16

D.  16 : 17

Correct Answer :

4 : 3

Explanation :
No Explanation available for this question

If A : B =8 : 15, B : C = 5 : 8 and C : D = 4 : 5, then A : D is equal to:

A.  2 : 7

B.  4 : 15

C.  8 : 15

D.  15 : 4

Correct Answer :

4 : 15

Explanation :
No Explanation available for this question

337.62 + 8.591 + 34.4 =?

A.  370.611

B.  380.511

C.  380.611

D.  426.97

Correct Answer :

380.611

Explanation :
No Explanation available for this question

The ratio between the whole expenses on taxes for every year and the entire expenses on fuel and transports for every year is around

A.  8:56

B.  4:12

C.  3:78

D.  10:13

E.  5:78

Correct Answer :

10:13

Explanation :
No Explanation available for this question

Which of the following fractions is less than 7/8 and greater than 1/3?

A.  1/4

B.  23/24

C.  11/12

D.  17/24

Correct Answer :

17/24

Explanation :
No Explanation available for this question