Aptitude Round QuestionRatio & ProportionFree Download
Conventional Method to Solve Ratio and Proportion Problems
The school book approach to this question uses the ratio and proportion
formulas and starts with assuming T (or any other variable) as the total
and then dividing it based on the relative division of the quantity between
the quantities.
Let the total amount be ‘T’
Step 1:
A’s share= (3/25)T, B’s share= (5/25)T, C’s share= (8/25)T, D’s share=
(9/25)T
Step 2:
D = A + 1872
Step 3:
(9/25)T = (3/25)T + 1872
Step 4:
(6/25)T = 1872
Step 5:
T = 1872 x (25/6)= 7800
Step 6:
B + C = (5/25)T + (8/25)T
Step 7:
B + C = (13/25)x 7800
Step 8:
B + C= 4056
Phew! Finally the correct answer after so many steps…
Smart Method to Solve Ratio and Proportion Problems
The above method may lead you to the correct answer but it’s a bad idea to
use it in exams where time is not your friend! A smart method is one which eliminates all extra calculations and steps.
We know that
A’s share= 3 parts, B’s share= 5 parts, C’s share= 8 parts, D’s share= 9
parts
Step 1:
Also we know D A= 1872= 9 parts – 3 parts= 6 parts= 1872
Step 2:
B + C = 13 parts
Step 3:
On Cross Multiplication we get B + C = 13 x (1872/6) = 4056
Rather than first get the value of whole, establish a relationship
between the given ratios and eliminate all redundant steps and
calculations.
Ratios and proportions and how to solve them
Let's talk about ratios and proportions. When we talk about the speed of a
car or an airplane we measure it in miles per hour. This is called a rate
and is a type of ratio. A ratio is a way to compare two quantities by using
division as in miles per hour where we compare miles and hours.
A ratio can be written in three different ways and all are read as "the
ratio of x to y"
xtoy
x
:y
xy
A proportion on the other hand is an equation that says that two ratios are
equivalent. For instance if one package of cookie mix results in 20 cookies
than that would be the same as to say that two packages will result in 40
cookies.
201=402
A proportion is read as "x is to y as z is to w"
xy
=zwwherey,w?0
If one number in a proportion is unknown you can find that number by
solving the proportion.
Example
You know that to make 20 pancakes you have to use 2 eggs. How many eggs are
needed to make 100 pancakes?

Eggs

pancakes

Small amount

2

20

Large amount

x

100

eggspancakes
=eggspancakesorpancakeseggs=pancakeseggs
If we write the unknown number in the nominator then we can solve this as
any other equation
x
100=220
Multiply both sides with 100
100·x100=100·220
x
=20020
x
=10
If the unknown number is in the denominator we can use another method that
involves the cross product. The cross product is the product of the
numerator of one of the ratios and the denominator of the second ratio. The
cross products of a proportion is always equal
If we again use the example with the cookie mix used above
201=402
1·40=2·20=40
It is said that in a proportion if
xy
=zwwherey,w?0
xw
=yz
If you look at a map it always tells you in one of the corners that 1 inch
of the map correspond to a much bigger distance in reality. This is called
a scaling. We often use scaling in order to depict various objects. Scaling
involves recreating a model of the object and sharing its proportions, but
where the size differs. One may scale up (enlarge) or scale down (reduce).
For example, the scale of 1:4 represents a fourth. Thus any measurement we
see in the model would be 1/4 of the real measurement. If we wish to
calculate the inverse, where we have a 20ft high wall and wish to reproduce
it in the scale of 1:4, we simply calculate:
20·1:4=20·14=5
In a scale model of 1:X where X is a constant, all measurements become 1/X
 of the real measurement. The same mathematics applies when we wish to
enlarge. Depicting something in the scale of 2:1 all measurements then
become twice as large as in reality. We divide by 2 when we wish to find
the actual measurement.
The ratio of two quantities a and b in the same units, is
the fraction and we write it as a : b.
In the ratio a : b, we call a as the first term
or antecedent and b, the second term or consequent.
Eg. The ratio 5 : 9 represents

5

with antecedent = 5, consequent = 9.

9

Rule:
The multiplication or division of each term of a ratio by the same nonzero
number does not affect the ratio.
Eg. 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.
The equality of two ratios is called proportion.
If a : b = c : d, we write a :b :: c : d and we say that a, b, c, d are in proportion.
Here a and d are called extremes, while b and c are called mean terms.
Product of means = Product of extremes.
Thus, a : b :: c : d ( b x c) = (a x d).
If a : b = c : d, then d is
called the fourth proportional to a, b, c.
Third Proportional:
a
: b = c : d, then c is called the third
proportion to a and b.
Mean Proportional:
Mean proportional between a and b is ab.
We say that (a : b) > (c : d)

a

>

c

.

b

d

Compounded Ratio:
The compounded ratio of the ratios: (a : b), (c
: d), (e : f) is (ace : bdf).
Duplicate ratio of (a : b) is (a^{2} : b^{2}).
Subduplicate ratio of (a : b) is (a : b).
Triplicate ratio of (a : b) is (a^{3} : b^{3}).
Subtriplicate ratio of (a : b) is (a ^{1/3} : b^{1/3}).
If

a

=

c

, then

a
+ b

=

c
+ d

. [componendo and dividendo]

b

d

a
 b

c
 d

We say that x is directly proportional to y, ifx = ky for some constant k and we write, x y.
We say that x is inversely proportional to y, if xy = k for some constant k and
1.

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:
A : B = 3 : 2.
B's share = Rs.


1210 x

2


= Rs. 484.

5


2.

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

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


3.

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. 2 x, Rs. 4x and Rs. 3x
respectively.
Then, 4x  3x = 1000
x
= 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

4.

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 8 x 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

The required ratio = 7x :

21x

: 14x

2

14x : 21x : 28x
2 : 3 : 4.

5.

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

20 + x = 80
x
= 60.
Quantity of water to be added = 60 litres.

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