1.

Ratio between two numbers is 3 : 2 and their difference is 225, then the smaller number is:

**Answer: Option 'B'**

**Given, the ratio of two numbers = 3 : 2
Let the two numbers be 3x and 2x
Given, their difference = 225
=> 3x - 2x = 225
=> x = 225
**

2.

One-third of the contents of a container evaporated on the 1st day, three-fourths of the remaining evaporated on the second day. What part of the contents of the container is left at the end of the second day?

**Answer: Option 'D'**

**After first day, 2/3 rd of the contents remain (i.e., 1 - (1/3) = 2/3)
After second day 2/3 (3/4) x (2/3) = 1/6 of the content remains**

3.

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

**Answer: Option 'A'**

**Let the Two numbers be A, B
40% of A = 2/3 B
Then, 40A /100 = 2B/3
=> 2A/5 = 2B/3
=> A/B = (2/3 x 5/2 ) = 5/3
Therefore, **

4.

Find the mean proportional between 49 & 81?

**Answer: Option 'C'**

**Formula = √a×b
A = 49 and B = 81
√49×81 = 7 × 9 = 63**

5.

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

**Answer: Option 'C'**

**Given
Sum = Rs. 53
Suppose C gets Rs. x
Then, B gets Rs. (x + 8) and A gets Rs. (x + 15)
⇒ x + x + 8 + x + 15 = 53
∴ 3 x = 53 - 8 - 15
3 x = 30
x = 30 / 3
x = 10
C = 10
B = ( 10 + 8 ) = Rs 18
C = ( 10 + 15) =Rs 25
So, A : B : C = 25 : 18 : 10**

6.

Two numbers are in the ratio 2:3. If eight is added to both the numbers, the ratio becomes 3:4. The numbers are

**Answer: Option 'B'**

**Numbers be m and n, m/n = 2/3 (m+8)/(n+8) = ? => m=16 and n= 24**

7.

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

**Answer: Option 'B'**

**Let the third number be x.
Then, first number = 120% of x = 1.2x = (6x/5)
Second number = 150% of x = 1.5x =(3x/2)
Ratio of first two numbers = (6x/5) :(3x/2) => (6x/5) x (2/3x) =>(12x) / (15x) = 12/15
= 4/5
**

8.

Two numbers are in the ratio 7:9. If 12 is subtracted from each of them, the ratio becomes 3:5. The product of the numbers is:

**Answer: Option 'A'**

**Given, ratio of two numbers = 7: 9 Let two numbers be 7x and 9x
If 12 is subtracted from each number, => (7x -12) / (9x - 12) = 3/5 => 5(7x - 12) = 3(9x - 12) => 35x - 60 = 27x - 36 => 8x = 24 => x = 3
Product of the numbers = 7x × 9x = 7(3) × 9(3) = 21 × 27 = 567**

9.

A bag contains 5p,10p and Rs20p coins in the ratio of 1:2:4 respectively. If the total money in the bag is Rs.84/-. Find the number of 10p coins in that bag?

**Answer: Option 'A'**

**5paisa : 10paisa : 20paisa = 1 : 2 : 4 ---> coins ratio
= 5 : 20 : 80 ---> money ratio
5 paisa × 80 coins = Rs.4/-
10 paisa × 160 coins = Rs.16/-
Then 10 paisa coins in that bag = 160 cions**

10.

The ratio of number of boys and girls in a school of 720 students is 7:5. How many more girls should be admitted to make the ratio 1:1?

**Answer: Option 'A'**

**Given, boys : girls = 7 : 5
Let, the total number of boys = 7x and total number of girls= 5x
Given, total students = 720
=> 7x + 5x = 720
=> 12x = 720
=> x = 60
so, total number of boys = 7x = 7 * 60 = 420 and
total number of girls= 5x = 5 * 60 = 300
Let y be the number of girls added to make the ratio 1 : 1
=> 420 / (300 + y) = 1/1
=> 420 = (300 + y)
=> y = 420 - 300
=> y = 120
So, **

11.

Two numbers are in the ratio 1:2, if 20 is added to each they are in the ratio 11:18. Find the two numbers.

**Answer: Option 'A'**

**Numbers are in the ratio 1 : 2
Two numbers are 1k and 2k
Adding 20 to both the numbers, 1k+20 and 2k+20
Given that 1k+20 : 2k+20 = 11 : 18 => 18(1k+20) = 11(2k+20) => (18-22)k = 20 x (-7) => k = 35
First Number , 1 x k = 35 Second Number 2 x k = 70
Numbers are 35 and 70**

12.

If A:B = 3:2 B:C= 4:3 then A:B:C=?

**Answer: Option 'A'**

**(6:4:3)**

13.

Find the fourth proportional to 2.4, 4.6 and 7.6?

**Answer: Option 'D'**

**Formula = Fourth propotional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56**

14.

A mixture contains milk and water in the ratio 3:2. If 4 liters of water is added to the mixture, milk and water in the mixture becomes equal. The quantity of milk in the mixture in liter is?

**Answer: Option 'B'**

**Given, Milk and Water ratio = 3 : 2
=> quantity of milk= 3x liters
quantity of water = 2x liters
If 4 liters of water is added to the mixture,
New Milk and Water ratio = 1 : 1 (Since equal),
quantity of milk in the new mixture,= 3x liters
quantity of water in the new mixture = 2x + 4 liters.
=>quantity of Milk in new mixture/ quantity of water in new mixture = 1 / 1
=> 3x / (2x + 4) = 1 / 1
=> 3x = (2x + 4)
=> 3x - 2x = 4
=> x = 4
Thus,quantity of milk= 3x liters = 3 × 4 = 12 liters**

15.

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

**Answer: Option 'B'**

**Let the third number be x.
Then, first number = 120% of x = 1.2x = (6x/5) Second number = 150% of x = 1.5x =(3x/2)
Ratio of first two numbers = (6x/5) : (3x/2) = 12/15 = 4/5
Ratio is 4 : 5**

16.

If the ratio of boys to girls in a class is B and the ratio of girls to boys is G, then 3 (B + G) is

**Answer: Option 'C'**

**Boys = x, Girls = y x/ y = B and y/x = G 3(B+G) = 3( y/x + x/y = 3 (x2+y2)/xy > 3**

17.

If a:b=5:3, b:c=5:4 and c:d = 11:5 then find a:b:c:d

**Answer: Option 'A'**

**a:b = 5x 5 : 3x 5 = 25 : 15 b:c = 5x 3 : 3x 4 = 15 : 12 a:b:c = 25 : 15 : 12
a x 11:b x 11:c x 11 = 275 : 165 : 132
c:d = 11:5 => c x 12 : d x 12 = 132:60
a:b:c:d = 275:165:132:60**

18.

Two vessels of equal volumes contains milk and water mixed in the ratio 1:2,2:3. When These mixtures are mixed to form a new mixture, what is the ratio of milk and water?

**Answer: Option 'A'**

**1:2 , 2:3
1/3:2/3 , 2/5:3/5
= 1/3 + 2/5 : 2/3 + 3/5
= 11/15 : 19/15 = 11 : 19 **

19.

The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?

**Answer: Option 'B'**

**5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27 **

20.

Two numbers are in the ratio of 1:2. If 7 be added to both, their ratio changes to 3:5. The greater number is

**Answer: Option 'B'**

**Let the two numbers be a, b.
Given, ratio b/w two numbers = 1 : 2
=> a / b = 1 / 2
=> **

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