Ration and Proportion Examples

Exercise :

1. Divide Rs. 580 between A and B in the ratio of 14:15.

Soln:A:B = 14:15 => 580 is divided into 29 equal parts => each part = Rs. 20.

So A’s share = 14 parts = 14 x 20 = Rs. 280

B’s share = 15 parts = Rs. 300.

2.If A:B = 2:3 and B:C = 4:5 then find A:B:C.

Soln:

To combine two ratios the proportions common for them shall be in equal parts. Here the common proportion is B for the given ratios.

Making B equal in both ratios they become 8:12 and 12:15 => A:B:C = 8:12:15.

3. Three numbers are in the ratio of 3: 4 : 8 and the sum of these numbers is 975. Find the three numbers.

Soln:Let the numbers be 3x, 4x and 8x. Then their sum = 3x+4x+8x = 15x = 975 => x = 65.

So the numbers are 3x = 195, 4x = 260 and 8x  = 520.

4. Two numbers are in the ratio of 4 : 5. If  the difference between these numbers is 24, then find the numbers.

Soln:Let the numbers be 4x and 5x. Their difference = 5x – 4x = x = 24 (given).

So the numbers are 4x = 96 and 5x = 120.

5. Given two numbers are in the ratio of 3 : 4. If 8 is added to each of them, their ratio is changed to 5 : 6. Find two numbers.

Soln:Let the numbers be a and b.

A:B = 3:4 => A / B = 3 / 4.

Also, (A+8) / (B+8) = 5 / 6.

Solving we get, A=12 and B = 16

6. A garrison has provisions for 120 soldiers for 240 days. After 180 days 60 more soldiers will join the group. For how many more days will the provisions last?

Soln:Actually after 180 days,

If 120 members are there provisions come for 60 more days (since total 240 days)

But now 180 members are there.

So number of days = (120/180) X 60 = 40 days.

7. If 24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs a day do it?

Soln:24 men – 12 hrs – 16 days

8 men – 6 hrs – ? days (n)

n =16 X (12 / 6) X (24 / 8)    ( since no of hrs reduced no of days has to increase and no of men reduced also increases no of days i.e., inverse proportional)=> n = 96 days.

8. 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

Solution : 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.

9. 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

Solution :

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.

10. 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

Solution : 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