1.

Find the fourth proportional to 2.4, 4.6 and 7.6?

2.

Find the third proportional to 9 and 12?

3.

Find the mean proportional between 49 & 81?

4.

Find the fourth proportional to 0.2,0.12 and 0.3?

5.

If a:b=1:2 and b:c=3:4 find a:b:c?

6.

If a:b=1:2, b:c=3:4 and c:d = 2:3 find a:b:c:d?

**Answer: Option 'B'**

**a:b = 1:2, b:c = 3:4, c:d = 2:3
1:2
3:4
( a = 1 × 3 = 3, b = 2 × 3 = 6 and c = 2 × 4 = 8)
(a = a × b, b= b × b and c= b × c)
a:b:c = 3:6:8
a:b:c = 3:6:8 and c:d = 2:3
(Note: First a,b,c multiplication with c means 2 and last c means 8
multiplication with d means 3
a:b:c:d = 6:12:16:24 **

7.

If a:b=2:3, b:c=4:5 and c:d=4:2 find a:b:c:d?

**Answer: Option 'D'**

**a:b = 2:3, b:c = 4:5, c:d = 4:2
2:3
4:5
( a = 2× 4 = 8, b = 37 × 4 = 12 and c = 3 × 5 = 15)
(a = a × b, b = b × b and c = b × c)
a:b:c = 8:12:15
a:b:c = 8:12:15 and c:d = 4:2
(Note: First a=8,b=12,c=15 multiplication with c means 4 and last c = 15
multiplication with d means 2
a:b:c:d = 32:48:60:30 **

8.

If 2a=6b and 9b=7c, Find a:b:c?

9.

If 0.4:1.4 :: 1:4:x, then x=?

10.

If x:y=5:3 then (8x-5y) : (8x+5y)=?

11.

A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?

12.

The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?

13.

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

14.

Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?

15.

If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?

**Answer: Option 'B'**

**2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
Short cut method:
a:b = 2:3
c:d = 3:4
1.Cross multiplication with both ratios a × d ~ b × c = 2 * 4 ~ 3 × 3 = 8 ~ 9 = 1
2. If 10 is added both the number means 10 × 3 = 30 and 10 × 4 = 40,
Then 30 ~ 40 = 10
=> 1 ---> 10
=> 2 ---> 20
**

16.

If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?

**Answer: Option 'D'**

**2:3
2x + 10 : 3x + 10 = 5 : 7
7[2x + 10] = 5[3x + 10]
14x + 70 = 15x + 50
15x - 14x = 70 - 50
x = 20
Then the first number is = 2
2x = 40
**

17.

If two numbers are in the ratio 5:3. If 10 is Reduced to both of the numbers then the ratio becomes 2:1 then find the smallest number?

**Answer: Option 'C'**

**5:3
5x - 10 : 3x - 10 = 2 : 1
1[5x - 10] = 2[3x - 10]
5x - 10 = 6x - 20
6x - 5x = 20 - 10
x = 10
the small number is = 3
3x = 30 (Answer = 30)
**

18.

A mixture contains milk and water in the ratio 5:2. On adding 10 liters of water, the ratio of milk to water becomes 5:3. The quantity of milk in the original mixture is?

**Answer: Option 'A'**

**milk:water = 5:2
5x : 2x + 10 = 5 : 3
3[5x] = 5[2x + 10]
15x = 10x + 50
15x - 10x = 50
x = 10
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7x = 70
**

19.

A mixture contains milk and water in the ratio 7:3. On adding 20 liters of water, the ratio of milk to water becomes 7:5. Total quantity of milk & water before adding water to it?

**Answer: Option 'B'**

**milk:water = 7:3
7x : 3x + 20 = 7 : 5
5[7x] = 7[3x + 20]
35x = 21x + 140
35x - 21x = 140
14x = 140
x = 10
The quantity of milk in the original mixture is = 7 : 3 = 7 + 3 = 10
10x = 100
**

20.

A mixture contains milk and water in the ratio 3:2. On adding 10 liters of water, the ratio of milk to water becomes 2:3. Total quantity of milk & water before adding water to it?

**Answer: Option 'C'**

**milk:water = 3:2
after adding 10 liters of water
milk:water = 2:3
Olny water patrs increase when mixture of water
milk:wate = 3:2 = 2*(3:2) = 6:4
after adding 10 liters of water
milk:water = 2:3 = 3*(2:3) = 6:9
milk parts always same
**

21.

If Rs.900/- Rupees are divided among a,b and c in such a way that A’s share 3 times that of B and B’s share is 2 times that of C. The A’s share is?

22.

If Rs.800/- Rupees are divided among a,b and c in such a way that A’s share 4 times more than B, B’s share is 3 times more than C. The C’s share is?

23.

If Rs.540/- are divided among A,B and C in such a way that A’s share is ½nd of B share and B’s share is 1/3rd of C’s share. The share of A is?

24.

If Rs.1440/- are divided among A,B and C so that A receives 1/3rd as much as B and B receives 1/4th as much as C. The amount B received is:

25.

Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?

26.

A bag contains 50p,Rs.1/- and Rs2/- coins in the ratio of 4:2:1 respectively. If the total money in the bag is Rs.60/-. Find the number of 50p coins in that bag?

27.

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?

28.

A bag contains 5p,10p and Rs20p coins in the ratio of 4:2:1 respectively. If the total money in the bag is Rs.30/-. Find the number of 5p coins in that bag?

29.

The ratio of first and second class train fares between two stations is 40:1 and that of the number of passengers travelling between these stations by first and second class is 1:20. If on a particular day Rs.2700/- be collected from the passengers travelling between these stations, then the amount collected from first class passengers is:?

30.

If a dozen mirrors are fallen down. The ratio between broken and unbroken mirrors is:

31.

Rs.4800/- are divided among P,Q and R in such a way that the share of P is 5/11 of the combined share of Q and R. Thus, P gets:?

32.

Rs.4800/- are divided among P,Q and R in such a way that the share of P is 5/11 of the combined share of Q and R. The share of Q is 3/13 of the combined share of R and P. Thus, R gets:?

33.

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?

34.

A person spends one-third of the money with him on clothes, one-fifth of the remaining on food and one-fourth of the remaining on travel. Now, he is left with Rs. 100. How much did he have with him in the beginning?

**Answer: Option 'B'**

**Initial amount be x.
Money spent on cloths = x/3.
Balance = x - (x/3) = 2x/3
Money on food, (1/5) x(2x/3) = 2x/15
Balance = (2x/3) - (2x/15) = 8x/15
Money spent on travel = (1/4) x (8x/15) = 2x/15
Balance = (8x/15) - (2x/15) =6x/15 = 2x/5
Given,2x/5 = 100
=> x = 250
Thus, the initial amount be Rs. 250**

35.

Rs. 770 have been divided among A, B and C such that A receives two-ninths of what B and C together receive. Then A’s share is:

36.

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?

37.

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

38.

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by

39.

Radhika purchased one dozen bangles. One day she slipped on the floor fell down. What cannot be the ratio of broken to unbroken bangles?

40.

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

41.

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

**Answer: Option 'D'**

**Quantity of milk = ( 60x2/3) 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 x litres.
Then, milk : water = (40/ 20 + x )
Now, (40/20 + x = 80 ) => x = 60
Therefore Quantity of water to be added = 60 litres.**

42.

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?

**Answer: Option 'A'**

**Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
=> (140 / 100 x 5x) , (150 /100 x 7x ) and (175 / 100 x 8x )
=> 7x , 21x/2 and 14x .
Therefore, ratio ofincreased seats
= 7x : (21x/2) : 14x
= 14x : 21x: 28x
=**

43.

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?

44.

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

45.

The ratio of the number of boys and girls at a party was 1:2 but when 2 boys and 2 girls left,the ratio became 1:3. Then the number of persons initially in the party was:

46.

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?

47.

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?

48.

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:

**Answer: Option 'C'**

**Let the three numbers be A, B, C.
Then, A : B = 2 : 3 and
B : C = 5 : 8
Now, A : B = 2 : 3
=> A : B = (2 × 5) : (3 × 5) = 10 : 15
Now, B : C = 5 : 8
=> B : C = (5 × 3) : (8 × 3) = 15 : 24
Thus, A : B : C = 10 : 15 : 24
=> A = 10x, B = 15x, C = 24x
Given, A + B + C = 98
=> 10x + 15x + 24x = 98
=> 49x = 98
=>**

49.

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:

50.

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

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