# Ratios and Proportions (114 Questions with Explanation)

1.

Find the fourth proportional to 2.4, 4.6 and 7.6?

A.) 14
B.) 14.657
C.) 15.56
D.) 14.56

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

2.

Find the third proportional to 9 and 12?

A.) 9
B.) 108
C.) 16
D.) 9

Formula = Third proportional = (b × b)/a
A = 9 and B = 12
(12 × 12)/ 9 = 144/9 = 16

3.

Find the mean proportional between 49 & 81?

A.) 16
B.) 10
C.) 63
D.) 12

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

4.

Find the fourth proportional to 0.2,0.12 and 0.3?

A.) 0.13
B.) 0.18
C.) 0.8
D.) 0.15

Formula = Fourth propotional = (b × c)/a
A = 0.2 , B = 0.12 and C = 0.3
(0.12 × 0.3)/0.2
0.036/0.2 = 0.18

5.

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

A.) 3:8:6
B.) 3:12:6
C.) 3:6:8
D.) 1:2:4

a:b = 1:2, b:c = 3:4
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

6.

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

A.) 3:6:8:24
B.) 6:12:16:24
C.) 6:18:24:16
D.) 3:6:2:3

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?

A.) 32:48:8:24
B.) 8:12:60:24
C.) 32:18:24:30
D.) 32:48:60:30

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?

A.) 42:18:14
B.) 3:9:7
C.) 9:27:22
D.) 21:7:9

(2a = 6b => a/b = 6/2)
and (9b = 7c => b/c = 7/9)
=> a:b = 6:2 and b:c = 7:9
a:b:c = 42:14:18 = 21:7:9

9.

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

A.) 49
B.) 4.9
C.) 0.49
D.) 0.4

0.4 × x = 1.4 × 1.4
x = 1.4 × 1.4/0.4 = 14/10 × 14/10 × 1/(4/10)
14/10 × 14/10 × 10/4
7/10 × 7 = 49/10 = 4.9

10.

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

A.) 5:13
B.) 13:5
C.) 5:11
D.) 11:5

x/y = 5/3 (Given)
(8x − 5y)/(8x + 5y)
8(x/y) − 5/8(x/y)+5
( on dividing Nr and Dr by y)
(8(5/3) − 5)/(8(5/3) + 5)
(40/3 − 5/1)/(40/3 + 5/1)
[(40 − 15)/3]/[(40 + 15)/3]
25/55 = 5/11
(8x-5y):(8x+5y) = 5:11

11.

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

A.) 7/45
B.) 1/35
C.) 45/7
D.) 5/21

Let the fraction be x. Then,
x:1/27 = 3/7 : 5/9
x × 5/9 = 1/27 × 3/7
x × 5/9 = 1/9 × 1/7
x × 5/9 = 1/63
x × 5 = 9/63
5x = 1/7 = 1/35

12.

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

A.) 8
B.) 12
C.) 14
D.) 16

3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ----> 4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)

13.

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

A.) 12
B.) 27
C.) 15
D.) 29

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

14.

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

A.) 16
B.) 8
C.) 12
D.) 24

= 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 × 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 × 6 = 24)

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?

A.) 10
B.) 20
C.) 30
D.) 40

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?

A.) 30
B.) 10
C.) 60
D.) 40

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
Short cut method:
a:b = 2:3
c:d = 5:7
1.Cross multiplication with both ratios a × d ~ b × c = 2 × 7 ~ 3 × 5 = 14 ~ 15 = 1
2. If 10 is added both the number means 10 × 5 = 50 and 10 × 7 = 70,
Then 50 ~ 70 = 20
==> 1 ---> 20
==> 2 ---> 40 (Answer is = 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?

A.) 10
B.) 20
C.) 30
D.) 40

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)
Short cut method:
a:b = 5:3
c:d = 2:1
1.Cross multiplication with both ratios a × d ~ b × c = 5 × 1 ~ 3 × 2 = 5 ~ 6 = 1
2. If 10 is reduced both the number means 10 × 2 = 20 and 10 × 1 = 10,
Then 20 ~ 10 = 10
=> 1 ---> 10
=> 3 ---> 30 (Answer is = 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?

A.) 70
B.) 50
C.) 30
D.) 40

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
Short cut method:
milk:water = 5 :2
after adding 10 liters of water
milk:water = 5 :3
milk is same but water increse 10liters then the water ratio is increse 1 parts
1 part ---> 10 liters
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7 parts ---> 70 liters  (Answer is = 70)
Short cut method - 2 : for Only milk problems
milk : water
5 : 2
5 : 3
milk ratio same but water ratio 1 part incress per 10 liters
1 part of ratio ---> 10 liters
7 part of ratio ---> 70 liters

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?

A.) 10
B.) 100
C.) 70
D.) 30

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
Short cut method:
milk:water = 7 : 3
after adding 20 liters of water
milk:water = 7 : 5
milk is same but water increse 20liters then the water ratio is increse 2 parts
1 part ---> 10 liters
The quantity of milk in the original mixture is = 7 : 3 = 7 + 3 = 10
10 parts ---> 100 liters  (Answer is = 100)
Short cut method - 2 : for Only milk problems
milk : water
7 : 3
7 : 5
milk ratio same but water ratio 2 parts incress per 20 liters
2 part of ratio ---> 20 liters
1 part of ratio ---> 10 liters
10 part of ratio ---> 100 liters

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?

A.) 10
B.) 50
C.) 20
D.) 40

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
Short cut method:
milk:water = 6 : 4
after adding 10 liters of water
milk:water = 6 : 9
milk is same but water increse 10liters then the water ratio is increse 5 parts
5 part ---> 10 liters
The quantity of milk in the original mixture is = 6 : 4 = 6 + 4 = 10
10 parts ---> 20 liters  (Answer is = 20)
Short cut method - 2 : for Only milk problems
milk : water
6 : 4
6 : 9
milk ratio same but water ratio 5 parts incress per 10 liters
5 part of ratio ----> 10 liters
10 part of ratio ---> 20 liters

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?

A.) Rs.600/-
B.) Rs.100/-
C.) Rs.200/-
D.) Rs.700/-

A:B:C = 6:2:1
Total parts = 9
A's share is = 6 parts
9 -----> Rs.900/-
6 -----> Rs.600/-

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?

A.) Rs.650/-
B.) Rs.600/-
C.) Rs.150/-
D.) Rs.50/-

A:B:C = 12:3:1
Total parts = 16
C's share is = 1 parts
16 -----> Rs.800/-
1 -----> Rs.50/- (Answer = Rs.50/-)

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?

A.) Rs.80/-
B.) Rs.360/-
C.) Rs.60/-
D.) Rs.120/-

A:B:C = 1:2:6
Total parts = 9
A's share is = 1 parts
9 -----> Rs.540/-
1 -----> Rs.60/-

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:

A.) Rs.90/-
B.) Rs.270/-
C.) Rs.1080/-
D.) Rs.27/-

A:B:C = 1:3:12
Total parts = 16
B's share is = 3 parts
16 -----> 1440
1 -----> 90
3 -----> 270 (B's share is 270)

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:?

A.) Rs.150/-
B.) Rs.200/-
C.) Rs.160/-
D.) Rs.255/-

A:B:C = 3:4:5
Total parts = 12
A's share is = 3 parts
12 -----> Rs.600/-
3 -----> Rs.150/-
A's total = 150 + 10 = Rs.160/-

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?

A.) 60 coins
B.) 10 coins
C.) 20 coins
D.) 40 coins

50paisa : Rs.1/- : Rs.2/- = 4 : 2 : 1  ---> coins ratio
= 2 : 2 : 2 ----> money ratio
Rs.2/- × 10 coins = Rs.20/-
Rs.1/- × 20 coins = Rs.20/-
50 Paisa × 40 coins = Rs.20/-
Then 50paisa coins in that bag = 40 cions

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?

A.) 160 coins
B.) 20 coins
C.) 128 coins
D.) None of these

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

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?

A.) 100 coins
B.) 150 coins
C.) 200 coins
D.) 250 coins

5paisa : Rs.10/- : Rs.20/- = 4 : 2 : 1  ---> coins ratio
=  1 : 1 : 1 ----> money ratio
3 ---> 30
1 ---> Rs.10/- × 20 coins ( 1/- = 5paisa × 20 cions )
Rs.10/-  = 200 coins(5paisa)

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:?

A.) Rs.1800/-
B.) Rs.600/-
C.) Rs.900/-
D.) Rs.600/-

First class:Second class = 40:1
mens ratio = 1:20
Tickets ratio = 40 : 1
Mens ratio = = 1 : 20
Money ratio = = 40 : 20 ==> 2 : 1
3 parts -----> Rs.2700/-
1 part -------> Rs.900/-
2 parts ------> Rs.1800/-

30.

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

A.) 2:3
B.) 3:4
C.) 5:7
D.) 5:4

Dozen means = 12
12/(2+3) = 12/5 ==> wrong
12/(3+4) = 12/7 ==> wrong
12/(5+7) = 12/12 = 1 ==> Right (Answer = 5:7)

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:?

A.) Rs.300/-
B.) Rs.3300/-
C.) Rs.1800/-
D.) Rs.1500/-

P/(Q+R) = 5/11
16 ----> Rs.4800/-
1 -----> Rs.300/-
P = 5 parts
5 ------> Rs.1500/- P = 300 × 5 = Rs.1500/-

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:?

A.) Rs.300/-
B.) Rs.3300/-
C.) Rs.1500/-
D.) Rs.2400/-

P/(Q+R) = 5/11
Q/(R+P) = 3/11
P:Q:R = 5:3:8
16 -------> Rs.4800/-
1 --------> Rs.300/-
R = 8 parts
R = Rs.300/- × 8 = Rs.2400/-

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?

A.) 11:19
B.) 19:11
C.) 2:5
D.) None of these

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

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?

A.) 200
B.) 250
C.) 300
D.) 450

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:

A.) Rs. 140
B.) Rs. 154
C.) Rs. 165
D.) Rs. 170

Given, A = (2/9) (B+C)
=>(B+C) = 9A / 2
Given, A + B + C = 770
=>A + 9A/2 = 770
=> 11A = 770 x 2
=> A = 70 x 2 = 140

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?

A.) One-fourth
B.) One-sixth
C.) One-half
D.) One-eighteenths

After first day, 2/3 rd of the contents remain After second day 2/3 – (3/4) x (2/3) = 1/6 of the content remains

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

A.) Equal to 3
B.) Less than 3
C.) More than 3
D.) Less than one-third

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

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

A.) One-ninth
B.) One-eighth
C.) One-seventh
D.) Seven-eighths

Given
When there are 8 people, the share of each person is 1/8
When there are 7 people, the share of each person is 1/7
Increase in the share of each person is
=>1/7 × 1/8
=> 1 / 56
Which if 1/7 of 1/8 of the original share of each person.
Share of each person = 1 / 7.

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?

A.) 1 : 2
B.) 2 : 3
C.) 1 : 5
D.) 1 : 3

There are totally 12 bangles,
Sum of the two numbers in the ratio should be a factor of 12,
Only 2:3 does not satisfy the criteria.

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

A.) 20
B.) 24
C.) 28
D.) 32

a/b = 1/2 and (a+7)/(b+7) = 3/5 => a= 14 and b = 28

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:

A.) 20 litres
B.) 30 litres
C.) 40 litres
D.) 60 litres

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?

A.) (2: 3: 4)
B.) (6: 7 : 8)
C.) (6 : 8: 9)
D.) (2 : 3 : 2 )

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
=2 : 3 : 4.

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?

A.) Rs. 500
B.) Rs. 1500
C.) Rs. 2000
D.) Rs. 1200

Let the shares of A, Band D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
=> x = 1000
Therefore B's share
= Rs. 2x
= Rs. (2 x 1000)
= Rs. 2000.

44.

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

A.) 4:05
B.) 2:05
C.) 6:07
D.) 3:05

Let the third number be x.
Then, first number = 120% of x
= 120x / 100
= 6 x / 5
Second number
= 150% of x
= 150 x / 100
= 3x / 2
Therefore, Ratio of first two numbers
= (6x /5 : 3x / 2 )
= 12x : 15x
= 4:5

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:

A.) 24
B.) 12
C.) 16
D.) 25

12

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?

A.) 21:22
B.) 8:09
C.) 17:18
D.) 8:11

Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x)
=> (120 / 100 x 7x ) and (110/ 100 x 8x )
=> 42x / 5 and 44x / 5
Therefore, The required ratio = ( 42 x/5 : 44x /5 ) = 42 : 44 = 21 : 22

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?

A.) Rs. 38,000
B.) Rs. 20,000
C.) Rs. 17,000
D.) Rs. 25,500

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, (2x+ 4000) / (3x + 4000) = 40 / 57
=> 57(2x + 4000) = 40(3x + 4000)
=> 6x = 68,000
=> 3x = 34,000
Sumit's present salary = (3x + 4000)
= Rs.(34000 + 4000)
= Rs. 38,000.

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:

A.) 38
B.) 42
C.) 30
D.) 28

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
=> x = 2
Thus, Second number, B = 15x = 15 × 2 = 30

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:

A.) 567
B.) 657
C.) 768
D.) 1575

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

50.

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

A.) 90
B.) 450
C.) 270
D.) 480