Ratio and Proportion
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 or antecedent and b, the second
term or consequent.
Example : The ratio 4 : 9
we can represent as 4 / 9 after this 4 is a antecedent and , consequent =
9
Rule of ration : In ratio
multiplication or division of each and every term of a ratio by the same non-
zero number does not affect the ratio.
Different type of
ratio problem is given in Quantitative Aptitude which is a very essential topic
in banking exam. Under below given some more example for your better
practice.
Anything we learn in
our school days was basics and that is well enough for passing our school
exams. Now the time has come to learn for our competitive exams. For this we
need our basics but also we have to learn something new. That’s where shortcut
tricks and formula are comes into action.
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 ).
Quiz on ratio and
proportion:-
1 If P : Q : R =
2 : 3 : 4 , Then P / Q : Q / R : R / P = ?
A. 8: 9: 24
B. 7: 9: 24
C. 4: 6: 15
D. 8: 11: 24
E. None of these
2: If 2P = 3Q =
4R, Then P : Q : R = ?
A. 2: 3: 5
B. 2: 3: 4
C. 3: 5: 6
D. 1: 2: 3
E. None of these
3: If P : Q = 2 :
3 , Q : R = 4 : 5 and R : S = 6 : 7 , then P : S = ?
A. 18: 25
B. 17: 35
C. 16: 35
D. 8: 11
E. None of these
4:Rama distributes his
pencil among his four friends Rakesh, Rahul, Ranjan, and Rohit in the ratio 1 /
2 : 1 / 3 : 1 / 4 : 1 / 5 . What is the minimum number of pencils that the
person should have?
A. 66
B. 64
C. 72
D. 77
E. None of these
5: Two numbers are
respectively 40% and 60% more than third number. Find the ration of two numbers
?
A. 8: 7
B. 7: 9
C. 9: 11
D. 8: 13
E. None of these
6: Rs 1210 were divided
among three person P, Q, R so that P : Q = 5 : 4 and Q : R = 9 : 10. Then R
gets the amount.
A. 450
B. 400
C. 500
D. 375
E. None of these
7: Share Rs.4200 among
joy, sanjay and bijoy in the ration 2 : 4 : 6.Find the amount received by
sanjay.
A. 1200
B. 1300
C. 1400
D. 1500
E. None of these
8 :Find the mean
proportional between given two number that is 64 and 49.
A. 45
B. 52
C. 54
D. 56
E. None of these
9: What number has to be
added to each term of 3 : 5 to make the ratio 5 : 6 .
A. 7
B. 6
C. 8
D. 5
E. None of these
10:Rs. 385 were divided
among P , Q , R in such a way that P had Rs 20 more than Q and R had Rs 15 more
than P . How much was R’s share?
A. 156
B. 145
C. 152
D. 150
E. None of these
Answers with
Explanation:-
1. P : Q : R = 2 : 3 : 4
.
Let
P = 2k,
Q
= 3k,
R = 4k.
Then,
Q
/ R = 3k / 4k = 3 / 4
R / P = 4k / 2k = 2 /
1.
2. Let 2P = 3Q =
4R = k ,
Then ,
P = k / 2,
Q
= k / 3 ,
R = k / 4.
SO , P : Q : R = k /
2 : k / 3 : k / 4 = 6 : 4 : 3.
3. (C)
4. Rakesh : Rahul :
Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we
need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among
friends,
Rakesh = ( 1 / 2 x 60
) = 30.
Rahul = ( 1 / 3 x 60
) = 20.
Ranjan = ( 1 / 4 x 60
) = 15.
Rohit = ( 1 / 5 x 60
) = 12.
For
minimum number of pencils x = 1 .
The person should
have atleast 77 pencils.
5.Step 1: Let the third
number is A
Then
first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of
B = 160 x B / 100 = 8B /5.
Step 2: now ratio of first and second number is 7A / 5 :
8B / 5 = 35A : 40B = 7 : 8.
6. P : Q = 5 : 4,
Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9.
So,
P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40
Sum of ratio terms is
= ( 45 + 36 + 40 ) =121.
R share of amount is
Rs (1210 x 40 / 121) = Rs. 400.
7. Amount received
by sanjay.
4
/ 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount
So, the Amount
received by sanjay is 1400.
8. The mean
proportion of two numbers is
Root
of 64 and 49 is √8 x √ 7 = 8 x 7 = 56.
So, the mean proportional is 56.
9.Let the number to be
added x , Then
3
+ x / 5 + x = 5 / 6
6 ( 3 + x ) = 5 ( 5 +
x )
x = ( 25 – 18 ) = 7
So , the number to be added is 7 .
10. Let Q gets Rs
x. Then We can say P gets Rs (x + 20 ) and R gets Rs ( x + 35) .
x
+ 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs 145 .
