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Basics of PROPORTION for Bank PO

Posted on - 11-04-2017

QA Math Proportion

Bank PO

Proportion

When two ratios are equal, the four quantities involved in the two ratios are said to be proportional i.e., if a/b = c/d, then a, b, c and d are proportional. This is represented as a : b :: c : d and is read as “a is to b (is) as c is to d”. .

When a, b, c and d are in proportion, then the items a and d are called the EXTREMES and the items b and c are called the MEANS. .

We also have the relationship,

Product of the MEANS = Product of the EXTREMES

i.e., bc = ad .

If a : b = c : d then

b : a = d : c → (1)

a : c = b : d

a + b : b = c + d : d → (2) obtained by adding 1 to both sides of the given relationship

a – b : b = c – d : d → (3) obtained by subtracting 1 from both sides of the given relationship

a + b : a – b = c + d : c – d → (4) obtained by dividing relationship (2) above by (3). .

Relationship (1) above is called INVERTENDO; (2) is called COMPONENDO; (3) is called DIVIDENDO and (4) is called COMPONENDO-DIVIDENDO. The last relationship, i.e., COMPONENDO-DIVIDENDO is very helpful in simplifying problems. .

Whenever we know a/b = c/d, then we can write (a + b)/ (a - b) = (c + d)/(c - d) by this rule. The converse of this is also true — wherever we know that (a + b)/(a - b) = (c + d)/(c - d), then wean conclude that a/b = c/d. .

If three quantities a, b and c are such that a : b : : b : c, then we say that they are in CONTINUED PROPORTION. We also get, b2 = ac. .

Worked out examples

EXAMPLE 1    

There are three, numbers, 6 times the first and seven times the second are equal. 5 times the second and 6 times the third are also equal. If the first number is 20 more than the third, find the third number. .

Solution

Let the first number, second number and third number be denoted as a, b and c respectively. .

6a = 7b
&⇒
a = b

5b = 6c
&⇒
c = b

a – c = 20
&⇒
b – b = 20


&⇒
b = 60
. .

c = = 50.

EXAMPLE 2

A bag has coins of denominations of one-rupee, two-rupees and five-rupees in the ratio 9 : 6 : 4. If the total value of five-rupee coins is Rs.32 more than the total value of two-rupee coins, find the total value of the coins in the bag. .

Solution

Let the number of coins of denominations of one-rupee, two-rupee and five-rupee be 9x, 6x and 4x respectively. Total value of coins 4(5x) - 6(2x) = 32 .

x = 4

Total value of the coins in the bag

9x + 12x + 20x

= 41x = Rs.164 .

x = 4

EXAMPLE 3

Calculate the fourth proportional to the numbers 0.8, 1.6 and 1.6. .

Solution

The fourth proportional of a, b, c is given by = 3.2

 
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