Ratio and Proportion

Question: The fourth proportional to 5, 8, 15 is:

[A].

18

[B].

24

[C].

19

[D].

20

Answer: Option B

Explanation:

Let the fourth proportional to 5, 8, 15 be x.

Then, 5 : 8 : 15 : x

5x = (8 x 15)

x =	(8 x 15)	= 24.
	5

Question: 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

Answer: Option D

Explanation:

Quantity of milk =		60 x	2	litres = 40 litres.
			3

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		=	1
		20 + x			2

20 + x = 80

x = 60.

Quantity of water to be added = 60 litres.

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

[A].

2 : 5

[B].

3 : 7

[C].

5 : 3

[D].

7 : 3

Answer: Option C

Explanation:

Let 40% of A =	2	B
	3

Then,	40A	=	2B
	100		3

	2A	=	2B
	5		3

	A	=		2	x	5		=	5
	B			3		2			3

A : B = 5 : 3.

Question:
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].

None of these

Answer: Option C

Explanation:

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then, 4x – 3x = 1000

x = 1000.

B’s share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

Question:
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].

8 : 9

[B].

17 : 18

[C].

21 : 22

[D].

Cannot be determined

Answer: Option C

Explanation:

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	x 7x		and		110	x 8x
		100					100

	42x	and	44x
	5		5

The required ratio =		42x	:	44x		= 21 : 22.
		5		5

Question:
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].

None of these

Answer: Option A

Explanation:

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	x 5x		,		150	x 7x		and		175	x 8x
		100					100					100

7x,	21x	and 14x.
	2

The required ratio = 7x :	21x	: 14x
	2

14x : 21x : 28x

2 : 3 : 4.

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

[A].

2 : 5

[B].

3 : 5

[C].

4 : 5

[D].

6 : 7

Answer: Option C

Explanation:

Let the third number be x.

Then, first number = 120% of x =	120x	=	6x
	100		5

Second number = 150% of x =	150x	=	3x
	100		2

Ratio of first two numbers =		6x	:	3x		= 12x : 15x = 4 : 5.
		5		2

Question:
A and B together have Rs. 1210. If of A’s amount is equal to of B’s amount, how much amount does B have?

[A].

Rs. 460

[B].

Rs. 484

[C].

Rs. 550

[D].

Rs. 664

Answer: Option B

Explanation:

	4	A	=	2	B
	15			5

A =		2	x	15	B
		5		4

A =	3	B
	2

	A	=	3
	B		2

A : B = 3 : 2.

B’s share = Rs.		1210 x	2		= Rs. 484.
			5

Question:
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].

20

[B].

30

[C].

48

[D].

58

Answer: Option B

Explanation:

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 =		5 x	3		:		8 x	3		= 3 :	24
			5					5			5

A : B : C = 2 : 3 :	24	= 10 : 15 : 24
	5

B =		98 x	15		= 30.
			49

Question: 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. 17,000

[B].

Rs. 20,000

[C].

Rs. 25,500

[D].

Rs. 38,000

Answer: Option D

Explanation:

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.

Then,	2x + 4000	=	40
	3x + 4000		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.