Ratio And Proportion Tips & Tricks

Ratio And Proportion Tips & Tricks

What is Ratio?
A ratio is a relationship between two numbers by division of the same kind. The ration of a to b is written as a : b = a / b In ratio a : b , we can say that a as the first term orantecedent and b, thesecond term or consequent.

Example :  The ratio 4 : 9 we can represent as  4 / 9 after this 4 is a antecedent and , consequent = 9

What is Proportion?
The idea of proportions is that two ratio are equal.
If a : b = c : d, we write a : b : : c : d,
Ex. 3 / 15 = 1 / 5
a and d called extremes, where as b and c called mean terms.
Proportion of quantities
the four quantities a, b, c, d said proportion then we can express it
a : b = c : d
Then a : b : : c : d  <–> ( a x d ) = ( b x c )
product of means = product of extremes.

If there is given three quantities like a, b, c of same kind then then we can say it proportion of continued.
a : b = b : c the middle number b is called mean proportion. a and c are called extreme numbers.
So, b2 = ac. ( middle number )2 = ( First number x Last number ).

 

Ratio Example 1

Example 1:
If P : Q : R = 2 : 3 : 4 , Then P / Q : Q / R : R / P = ?
 

Answer :
P : Q : R = 2 : 3 : 4 . Let P = 2k, Q = 3k, R = 4k. Then,
P / Q = 2k / 3k = 2 / 3 , Q / R = 3k / 4k = 3 / 4 and R / P = 4k / 2k = 2 / 1.
SO, P / Q : Q / R : R / P = 2 / 3 : 3 / 4 : 2 / 1 = 8 : 9 : 24 .
 

Example 2:
If P : Q = 2 : 3 and Q : R = 4 : 5 , then R : P = ?
 

Answer :
P / R = ( P / Q x Q / R ) = ( 2 / 3 x 4 / 5 ) = 8 / 15
=R / P = 15 / 8 = R : P = 15 : 8.

Ratio Example 2

Example 1 :
On dividing a sum of Rs 832 between Paul and john in the ratio 1 / 3 : 1 / 5 , their shares are :
 

Answer :
So the given ratio is = 1 / 3 : 1 / 5 = 5 : 3
So , the 1st part = Rs ( 832 x 5 / 8 ) = Rs 520 , 2nd part = Rs ( 832 x 3 / 8 ) = Rs 312
So , their shares are : 520 and 312 .

Example 2 :
The Salary of Three friend A, B, C are divided into ratio 5 : 6 : 8.If the increment has given of 10%, 20%, 25%, Find the new ratio of three friend salary ?
 

Answer :
Step 1: We assume ration as 5x, 6x, 8x
now the increment of new salary is A = 110 / 100, B = 120 / 100, C = 125 / 100.
 

Step 2: A,s new salary is 110 X 5x / 100 = 55x / 10.
B,s new salary is 120 X 6x / 100 = 36x / 5.
C,s new salary is 125 X 8x / 100 = 10.
 

Step 3:New ratio is 55x / 10 : 36x / 5 : 10.

Ratio Example 3

Example 1:
A money bag contains 50 p, 25 p, and 10 p coins in the ratio 5 : 9 : 4, and the total amounting to Rs.206.
Find the individual number of coins of each type.
 

Answer :
Step 1: Let the number of 50 p ,25 p, and 10 p coins be 5x, 9x, 4x respectively.
Then, 5x / 2 + 9x / 4 + 4x / 10 = 206
= 50x + 45x + 8x = 4120
= 103x = 4120
= x = 40.
 

Step 2: Number of 50 p coins is ( 5 x 40 = 200 ),
Number of 25 p coins is( 9 x 40 = 360 ),
Number of 10 p coins ( 4 x 40 = 160 ),

Example 2:
On a self there are 4 books on Economics , 3 books on Management and 4 books on Statistics . In how many different ways can be the books be arranged so that the books on Economics  are kept together ?
 

Answer :
( 4 books on Statistics ! + 3 books on Management ! + 1 x   4 books on Economics ! )
Total ways = 8! x 4!
= ( 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ) x ( 4 x 3 x 2 x 1 )
= 40320 x 24
= 967680 .
So , we can 967680 way be the books be arranged .

Ratio Example 4

Example 1 :
Milk and water in the ratio 5 : 3 is contain in a 20 litres of mixture . If 4 litres of this mixture be replaced by 4 litres of milk  , the ratio of milk to water in the new mixture would be ?
 

Answer :
Quantity of milk in a mix = ( 16 x 5 / 8 ) = 10 litres .
quantity of milk in 20 litres of new mix = ( 10 + 4 ) = 14 litres .
quantity of water in it ( 20 – 14 ) = 6 litres.
Ratio of milk and water in the new ratio mix is = 14 : 6 = 7 : 3

Example 2:
In a bottle mixture of 80 liters and the ratio of milk and water is 3 : 2. If this mixture ratio is to be 2 : 3.  What the quantity of water to be further added ?
 

Answer :
Step 1: Quantity of Milk ( 80 x 3 / 5 ) = 48 liters, So Quantity of water in it  ( 80 – 48 ) = 32 liters.

Step 2: New Ratio required 2 : 3, Let x water to be added, Then Milk : Water is = 48 : (32+x)
=48 / (32 + x).
Step 3: Now 48 / (32 + x) = 2 : 3
48 / (32 + x) = 2 / 3
2x = 144 – 64
x = 80/2
=40 liters.