Practice Ratio and proportion - quantitative aptitude Online Quiz (set-1) For All Competitive Exams

Q-1)   What number should be subtracted from both the terms of the ratio 11 : 15 so as to make it as 2 : 3 ?

(a)

(b)

(c)

(d)

Explanation:

Required number = x

${11 - x}/{15 - x} = 2/3$

33 - 3x = 30 - 2x

3x - 2x = 33 - 30

x = 3


Q-2)   In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?

(a)

(b)

(c)

(d)

Explanation:

Quantity of milk

= $7/10 × 80 = 56$ litres

Quantity of water

= $3/10 × 80$ = 24 litres

Let x litre water be added Then,

$56/{24 + x} = 2/1$

24 + x =28 ⇒ x = 4 litres


Q-3)   The mean proportional between $(3 +√2)$ and $(12 - √32)$ is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 14
Mean Proportion - Let x be the mean proportion between a and b, then a:x::x:b (Real condition)
$a/x = x/b ⇒ x^2 =ab$
$x =√{ab}$
So, mean proportion of a and b = $√{ab}$
If x be the mean proportion between (x - a) and (x - b) then what will be the value of x ?
$x = {ab}/{a+b}$

Mean proportional

=$√{(3+√2)(12-√{32})}$

= $√{(3+√2)4(3-√2)}$

= 2$√{9 - 2} = 2√7$


Q-4)   The present age of two persons are 36 and 50 years respectively. If after n years the ratio of their age will be 3 : 4, then the value of n is

(a)

(b)

(c)

(d)

Explanation:

${36 + n}/{50 + n} = 3/4$

144 + 4n = 150 + 3n

4n - 3n = 150 - 144

n = 6


Q-5)   The ratio between two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. The difference between the numbers is

(a)

(b)

(c)

(d)

Explanation:

Let the numbers be 3x and 4x.

${3x + 6}/{4x + 6} = 4/5$

16x + 24 = 15x + 30

x = 30 - 24 = 6

Required difference = 6

Using Rule 34
Two numbers are in the ratio a:b and if each number is increased by x, the ratio becomes c:d. Then the two numbers will be
${xa(c-d)}/{ad-bc}$ and ${xb(c-d)}/{ad-bc}$

Here, a = 3, b= 4, x = 6

c = 4, d = 5

The numbers are = ${xa(c-d)}/{ad-bc}$

= ${6.3(4 - 5)}/{3 ×5 - 4 × 4}$

= ${18 × -1}/{15 - 16}$ = 18

= ${xb(c-d)}/{ad-bc}$

= ${6 × 4(4 - 5)}/{3 × 5 - 4 × 4}$

= ${24 × (-1)}/{15 - 16}$ = 24

Numbers are 24 and 18.

Their difference = 24 - 18 = 6


Q-6)   The average of 11 numbers is 36, whereas average of 9 of them is 34. If the remaining two numbers are in the ratio of 2 : 3, find the value of the smaller number (between remaining two numbers).

(a)

(b)

(c)

(d)

Explanation:

According to the question,

Sum of remaining two numbers

= 11 × 36 - 9 × 34

= 396 - 306 = 90

Ratio of the remaining two numbers = 2 : 3

Smaller number

= $2/5$ × 90 = 36


Q-7)   The total number of students in a school was 660. The ratio between boys and girls was 13 : 9. After some days, 30 girls joined the school and some boys left the school and new ratio between boys and girls became 6 : 5. The number of boys who left the school is :

(a)

(b)

(c)

(d)

Explanation:

In the first case,

Boys = $660 × 13/22$ = 390

Girls = $660 × 9/22$ = 270

If x boys leave the school, then

${390 - x}/{270 + 30} = 6/5$

390 - x = 360

x = 390 - 360 = 30


Q-8)   The ratio of the number of ladies to that of gents at a party was 3 : 2. When 20 more gents joined the party, the ratio was reversed. The number of ladies present at the party was

(a)

(b)

(c)

(d)

Explanation:

Let the number of ladies and gents be 3x and 2x respectively.

According to the question,

${3x}/{2x + 20} = 2/3$

9x = 4x + 40

5x = 40 ⇒ x = 8

Number of ladies = 3x

= 3 × 8 = 24


Q-9)   In a bag, there are three types of coins — 1-rupee, 50 paise and 25-paise in the ratio of 3 : 8 : 20. Their total value is 372. The total number of coins is

(a)

(b)

(c)

(d)

Explanation:

Ratio of the number of coins of Re. 1, 50 paise and 25 paise

= 3 : 8 : 20

Ratio of the values of these coins

= $3 : 8/2 : 20/4$ = 3 : 4 : 5

Value of 1 rupee coins

= $3/12 × $372 = Rs.93

Value of 50 paise coins

= $4/12 × 372$ = Rs.124

Value of 25 paise coins

= $5/12$ × 372 = Rs.155

Number of coins

= 93 + 124 × 2 + 155 × 4

= 93 + 248 + 620 = 961


Q-10)   A bag contains 90 in coins of denominations of 50 paise, 25 paise and 10 paise. If coins of 50 paise, 25 paise and 10 paise are in the ratio 2 : 3 : 5, then the number of 25 paise coins in the bag is

(a)

(b)

(c)

(d)

Explanation:

Ratio of values of 50 paise, 25 paise and 10 paise coins

= $2/2 : 3/4 : 5/10$

= $1 : 3/4 : 1/2$ = 4 : 3 : 2

Sum of the ratios = 4 + 3 + 2 = 9 Value of 25 paise coins

= $3/9 × 90$ = Rs.30

Number of 25 paise coins

= 30 × 4 = 120


Q-11)   My grandfather was 9 times older than me 16 years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was

(a)

(b)

(c)

(d)

Explanation:

16 years ago,

My age = x years

My grandfather’s age = 9x years

After 8 years from the present,

9x + 16 + 8 = 3(x + 8 + 16)

9x + 24 = 3x + 24 + 48

9x + 24 = 3x + 72

9x - 3x = 72 - 24

6x = 48

$x = 48/6$ = 8

Required ratio 8 years ago,

= (x + 8) : (9x + 8)

= (8 + 8) : (9 × 8 + 8)

= 16 : 80 = 1 : 5


Q-12)   The ratio of the ages of a father and his son 10 years hence will be 5 : 3, while 10 years ago, it was 3:1. The ratio of the age of the son to that of the father today, is

(a)

(b)

(c)

(d)

Explanation:

Let the age of father 10 years hence is 5x years,

then age of son 10 years hence will be 3x years.

According to the question,

${5x - 10 - 10}/{3x - 10 - 10} = 3/1$

${5x - 20}/{3x - 20} = 3/1$

5x - 20 = 9x - 60

4x = 40 or x = 10

Required ratio

= (3x - 10) : (5x - 10)

= 20 : 40 = 1 : 2


Q-13)   The ratio of the present ages of two boys is 3:4. After 3 years, the ratio of their ages is equal to will be 4:5.The ratio of their ages after 21 years will be

(a)

(b)

(c)

(d)

Explanation:

Let the ages of boys be 3x and 4x years respectively.

According to the question,

After 3 years

${3x + 3}/{4x + 3} = 4/5$

16x + 12 = 15x + 15

16x - 15x = 15 - 12

x = 3

Required ratio after 21 years

= ${3x + 21}/{4x + 21}$

= ${3 ×3 + 21}/{4 × 3 + 21} = {9 + 21}/{12 + 21}$

= $30/33 = 10/11$


Q-14)   If 4 years ago the ratio between the ages of P and Q was 5 : 6 and the sum of their ages at present is 52 years, what is the ratio of their present ages ?

(a)

(b)

(c)

(d)

Explanation:

4 years ago,

P’s age = 5x years

Q’s age = 6x years

According to the question,

5x + 4 + 6x + 4 = 52

11x = 52 - 8 = 44

$x = 44/11$ = 4

Required ratio

= (5x + 4) : (6x + 4)

= (5 × 4 + 4) : (6 × 4 + 4)

= 24 : 28 = 6 : 7


Q-15)   The ratio between Sumit’s and Prakash’s age at present is 2 : 3. Sumit is 6 years younger than Prakash. The ratio of Sumit’s age to Prakash’s age after 6 years will be

(a)

(b)

(c)

(d)

Explanation:

Sumit’s present age

= 2x years

Prakash’s present age

= 3x years

3x - 2x = 6 ⇒ x = 6

Required ratio

= (2 × 6 + 6) : (3 × 6 + 6)

= 18 : 24 = 3 : 4


Q-16)   A container contains 60 kg of milk. From this container 6 kg of milk was taken out and replaced by water. This process was repeated further two times. The amount of milk left in the container is

(a)

(b)

(c)

(d)

Explanation:

Amount of milk left

= Initial amount ×

$(1-\text”Amount taken out in each operation”/\text”Initial amount”)^3$

= $60(1 - 6/60)^3$

= $60(1 - 1/10)^3$

= $60 × 9/10 × 9/10 × 9/10$

= 43.74 kg.


Q-17)   A mixture contains spirit and water in the ratio 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is

(a)

(b)

(c)

(d)

Explanation:

Let the amount of water be x litres.

Then, ${x + 3}/x = 3/2$

or 2x + 6 = 3x

or x = 6

The quantity of spirit in the mixture

= x + 3 = 6 + 3 = 9 litres


Q-18)   Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages 3:5?

(a)

(b)

(c)

(d)

Explanation:

Let x years ago the ratio of their age was 3 : 5

According to the question

${40 - x}/{60 - x}= 3/5$

200 - 5x = 180 - 3x

2x = 20

x = 10 years


Q-19)   At present, the ratio of the age of Maya and Chhaya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Maya’s present age is

(a)

(b)

(c)

(d)

Explanation:

Let Maya’s present age be 6x years and Chhaya’s present age be 5x years.

After 15 years,

${6x + 15}/{5x + 15} = 9/8$

48x + 120 = 45x + 135

48x - 45x = 135 - 120

3x = 15 ⇒ x = 5

Maya’s present age = 6x

= 6 × 5 = 30 years


Q-20)   The ratio of A’s age to B’s age is 4 : 3. ‘A’ will be 26 years old after 6 years. The age of B now is :

(a)

(b)

(c)

(d)

Explanation:

A’s present age

= 4x years (let).

According to the question,

4x + 6 = 26

4x = 26 - 6 = 20

$x = 20/4$ = 5

B’s present age

= 3x = 3 × 5 = 15 years