Ratio and Proportion- Aptitude Questions and Answers

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Ratio between three numbers is 1 : 2 : 3 and sum of their squares is 504. The numbers are?

A)
6, 12, 18

B)
3, 6, 12

C)
4, 8, 24

D)
2, 4, 8


Correct Answer :

6, 12, 18


Explanation :

Let the three numbers be x, 2x and 3x respectively
(x)2 + (2x)2 + (3x)2= 504
14x2 = 504
x2 = 36
x = 6
So, three numbers are respectively x, 2x and 3x that is 6, 12 and 18 .

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Priya broke her bangles as she slipped while walking. If she was wearing 12 bangles in her hands then which of the following cannot be the ratio of broken is to unbroken bangles?

A)
1 : 1

B)
1 : 2

C)
1 : 3

D)
1 : 4


Correct Answer :

1 : 4


Explanation :

the sum of ratio must be a factor of 12 (1 x 12, 2 x 6, and 3 x 4) , that is 1, 2, 3, 4, 6 and 12 . So, they cannot be in the ratio 1 : 4

The ratio of incomes of A and B is 4:3 and their expenditures are in the ratio 3:2. If A saves one third of his income then find the ratio of their savings?

A)
4:3

B)
9:7

C)
12:11

D)
4:5


Correct Answer :

12:11


Explanation :

Let, income of A and B are 4x and 3x,and their expenditure are 3y and 2y
then there saving are 4x - 3y and 3x - 2y
As given A save 1/3 rd of his income,then 4x - 3y = (1/3)*4x
12x - 9y = 4x
x = 9y/8

then ratio of their saving = (4x - 3y)/(3x - 2y)
= (36y/8 - 3y)/(27y/8 - 2y) after using x value
= (36y-24y) / (27y-16y)
= 12/11

The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 490, Krishan has ?

A)
Rs. 2890

B)
Rs. 2330

C)
Rs. 1190

D)
Rs. 2680


Correct Answer :

Rs. 2890


Explanation :

a : b : c = A : B : C is equivalent to ,a/A = b/B = c/C

Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Then, Ram : Gopal : Krishan = 49 : 119 : 289
⇒ Ram : Krishan = 49 : 289

Thus, 49 : 289 = 490 : X
X= 289 * 490 / 49
= Rs. 2890

If 8 : y = y : 18 , then y is equal to ?

A)
144

B)
72

C)
26

D)
12


Correct Answer :

12


Explanation :

a : b : c = A : B : C is equivalent to ,a/A = b/B = c/C

8 x 18 = y2
y = √144 = 12

The third proportional to 0.8 and 0.2 is ?

A)
0.4

B)
0.8

C)
0.05

D)
0.032


Correct Answer :

0.05


Explanation :

Third Proportional: If a: b = b: c, then c is called the third proportional to a and b.

Let 0.8 : 0.2 : : 0.2 : X
Then 0.8 x X = 0.2 x 0.2
Thus, C = ( 0.2 x 0.2) / 0.8 = 0.04 / 0.08 = 4/80 = 0.05

The fourth proportional to 0.2, 0.12 and 0.3 is ?

A)
0.13

B)
0.15

C)
0.18

D)
0.8


Correct Answer :

0.18


Explanation :

Fourth Proportional: If a : b = c: d, then d is called the fourth proportional to a, b, c.

Let 0.2 : 0.12 : : 0.3 : X
As, 0.2 * X = 0.12 * 0.3
Thus, X = (0.12 * 0.3) / 0.2 = 0.18

If A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, then A : D is equal to ?

A)
2 : 7

B)
7 : 8

C)
16 : 35

D)
4 : 13


Correct Answer :

16 : 35


Explanation :

(A/B) x (B/C) x (C/D) = (2/3) x (4/5) x (6/7) = 16/35
Thus, A : D = 16 : 35

A bag contains 25 paise, 10 paise and 5 paise coins in the ratio 1 : 2 : 3 . If their total value is 60, then the number of 5 paise coins is ?

A)
10

B)
50

C)
30

D)
40


Correct Answer :

30


Explanation :

Let the number of 25 paise, 10 paise and 5 paise coins be X, 2X and 3X, respectively. Then ,
X + 2X + 3X = 60
⇒ X = 10
Thus, The number of 5 paise coins = 3 x 10 = 30

Find the mean proportional between 9 and 64 ?

A)
25

B)
24

C)
27

D)
35


Correct Answer :

24


Explanation :

Mean Proportional: Mean proportional between a and b is square root of ab.

Mean proportional = √(9 x 64)
= 3 x 8 = 24

Two numbers are in the ratio of 7:9, if we subtract 14 from each number the ratio will become 5:7. Find the sum of both the numbers?

A)
112

B)
144

C)
128

D)
160


Correct Answer :

112


Explanation :

Let the numbers be 7x and 9x . When 14 is subtracted from both,then we get
(7x-14):(9x-14) :: 5:7
49x - 98 = 45x - 70
4x = 28
x = 7

So the numbers are 49 and 63 ,and their sum =(49+63)= 112

The ratio of the number customers visited to a mall to those who purchased the clothes is 11:4. On a particular day 1320 customers visited to the mall. How many of these purchased the clothes?

A)
320

B)
480

C)
360

D)
425


Correct Answer :

480


Explanation :

The ratio of number customers visited / customers who purchased the clothes =11 / 4

Let the X number of customers purchased the clothes
So , 1320 / X =11 / 4
X=1320*4 /11

Thus number of customers purchased the clothes ,X = 480

The ratio of expenditure and savings of a person is 26: 3. If his monthly income is 7250, then what is his monthly savings?

A)
290

B)
350

C)
750

D)
780


Correct Answer :

750


Explanation :

Let monthly expenditure = 26x and monthly savings = 3x
Then, monthly income = 26x + 3x = 29x
29x = 7250
x = 250
Monthly savings = 3 * 250 = 750

750 is distributed in A, B and C such that A : B = 5 : 2, B : C = 7: 13 then what is A's part?

A)
140

B)
250

C)
260

D)
350


Correct Answer :

350


Explanation :

A : B = 5 : 2 = 5/2 :1
B : C = 7 : 13 = 1 : 13/7
A : B : C = 5/2 :1 : 13/7 = 35 : 14 : 26
A's part =750 * (35/75) => 350

60 m of a uniform wire weight 80 kg. What will 141 m of the same wire weight?

A)
144

B)
188

C)
288

D)
282


Correct Answer :

188


Explanation :

60/80 =141/x
x = 188

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

A)
400

B)
540

C)
420

D)
360


Correct Answer :

360


Explanation :

Let the number of 50-paisa, 25-paisa & 10-paisa coins be 5x ,9x , 4x respectively
total amount = Rs.206
As is given, (0.50)(5x) + (0.25)(9x) + (0.10)(4x) = 206
x = 40

therefore,
No. of 50p coins, 5*40 = 200
No. of 25p coins, 9*40 = 360
No. of 10p coins, 4*40 = 160

In a bag, there are notes of 10, 20 and 50 in the ratio of 1 : 2 : 3. If the total money is 1000, how many notes of 10 are there?

A)
5

B)
10

C)
15

D)
30


Correct Answer :

5


Explanation :

Let the number of 10, 20 and 50 notes be X, 2X and 3X, respectively. Then ,
10*X + 40*X + 150*X = 1000
X = 5
So, the number of 10 notes are, X = 5

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