# Quantitative Aptitude > Ratio, Proportion and Variation

 Refresher Test - Ratio, Proportion and Variation Discuss

Practice Tests
 Practice Test - Ratio, Proportion and Variation Discuss

Ratio

Free Online Preparation for CAT 2009 with Minglebox e-CAT Prep. Cover basic concepts of Ratio, Proportion and Variation under Quantitative Aptitude for MBA Entrance Exam Preparation with Study material, solved examples and tests prepared by CAT coaching experts.

Ratio is a tool for comparing 2 quantities . For example in a clear if there are 20 girls and 30 boys then we can compare the number of boys and girls as follow:

which is offer stated as

Number of girls : Number of boys = 2 : 3

Number of girls =

Number of boys =

Ratio is a pure number it does not have a unit. The 2 numbers used in ratio are known as the 'terms' of the ratio. The first term is known as 'antecedent' and the second term is known as 'consequent'.

If the ratio of 2 or more quantities is given by

a:b:c

then actual quantity is given by

ak, bk, ck

where k is constant.

Proportion

Equality 2 ratio is known as proportionality that is if then a,b,c,d are in proportion similarly if . a, b, c, d,

e, f etc are in proportion.

If then

Solved Examples

Question

If then the value of is

Solution

As

a =

c =

e = putting values of a,c,ein the expression

= =

Question

The ratio of the current ages of Anita and Sunita is 4:3. 8 years hence, the ratio of their ages will be 6:5. then their current ages are

Solution

Let this current ages of Anita and Sunita be 4k and 3k then their ages 8 years hence will 4k+8, 3k+8 hence of their ages 8 years hence will be

Solving we get 20k + 40 = 18 k + 48

2k = 8

k = 4

Hence their current ages are 16 and 12 years respectively.

Question

An engine can pull on empty boogie at the speed of 18 k mph and the reduction in its speed is directly proportional to the square root of the number of boxes it can carry of equal weight of 10 kg each. If the speed of the engine is 12 k mph when 9 boxes are loaded in the boogie. Find the maximum weight that can be carried if the speed of the engine and boogie is to be maintained at least 10 k mph ?

Solution

It is given that speed of engine and boogie without any of the boxes = 18 k mph

If 'x' is the speed of the engine and boogie with the boxes loaded , then x = where k is a constant of proportionality n is the number of boxes loaded in the boogie.

From the given information we get

k = 2

putting the maximum number of boxes allowed is 16 and therefore weight is 160 kg

Question

Instead of walking along two adjacent sides of a rectangular field a man took a shot cut along the diagonal and saved a distance equal to the longer side - then the ratio of the shortcut side to the longer side is

1. 1/2
2. 2/3
3. 1/4
4. 3/4

Solution

Let l,b the length and breath of the rectangular field then length of diagonal of the field is given by according to given condition we

get (assuming l>b)

Squaring both side we get

Hence option (4) is the correct answer

Question

Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight . What is the weight of dry grapes available from 20 kg of fresh grapes ?

1. 2 kg

2. 2.4 kg

3. 2.5 kg

4. none of these

Solution

Let x kg be weight of dry grapes obtained from 20 kg of fresh grapes then weight of solid substance in fresh grapes will be same as in dried grapes hence we get

x = 2.5 kg

 Refresher Test - Ratio, Proportion and Variation Discuss

 Practice Test - Ratio, Proportion and Variation Discuss