Ratio and Proportion
**What is Ratio and Proportions ?
** Diff B/w Ratio and Proportions ?
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 antecedent =5, consequent
=9
Rule: The multiplication or division of each term of a
ratio by the same non-zero number does not affect the
ratio
Proportion:
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)
Example :
If 0.75 : x :: 5 : 8, then x is equal to:
A. 1.12
B. 1.20
C. 1.25
D. 1.30
Fourth Proportional:
If a : b = c : d, then d is called the fourth proportional
to a, b, c.
Third Proportional:
a : b = b : c, then c is called the third proportional
to a and b.
Mean Proportional:
Mean proportional between a and b is .
Duplicate Ratios:
Q.1 If A:B= 2:3 and B:C= 5:4 , find A:C
A)1:2
B)3:2
C)5:6
D)2:3
Q.2 If A:B=2:3, B:C=3:4, C:D=16:15. Find A:D
A) 15:8
B) 8:15
C) 1:2
D) 3:2
Q. Find the fourth proportion to 2,3,6
A) 18
B) 12
C) 9
D) 4
Q. Find the third proportion to 3,6
A) 18
B) 12
C) 9
D) 4
Examples on ratio And Proportions :
Q3. The ratio of A:B:C is 5:2:3
a) if the sum of B & C is 75 find the no.s
b) if the sum of A & B is 36 more than C, Find
A,B,C
c) If the product of B & C is 96 find the no.s
d) if B is 18, Find the no.s
Q4. The ratio of B & G is 10:3, when 36 girl more
joined the ratio becomes 10:7. Find the no. of boys?
A. 90
B. 100
C. 60
D. None
Q 5. The income ratio of A & B is 5:8, if income of A
increases by 60000, then the new ratio is 5:4, Find
current income of A.
A.120000
B.240000
C.360000
D.None
Q6. Ratio of boys and girl is 4:5 when 100 girl left
the ratio becomes 6:7, find no. of boys
A. 1200
B. 600
C. 800
D. None
Q7. The ratio of the number of boys and girls in a
college is 7 : 8. If the percentage increase in the
number of boys and girls be 20% and 10%
respectively, what will be the new ratio?
A.8 : 9
B.17 : 18
C.21 : 22
D.Cannot be determined
Q8. If Rs. 782 be divided into three parts,
proportional to 1/2: 2/3 : 3/4, then the first part is:
A.Rs. 182
B.Rs. 190
C.Rs. 196
D.Rs. 204
Q9. The fourth proportional to 5, 8, 15 is:
A.18
B.24
C.19
D.20
Q10. In a bag, there are coins of 25 p, 10 p and 5 p in
the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how
many 5 p coins are there?
A.50
B.100
C.150
D.200
Q.11 A and B together have Rs. 1210. If 4/15 of A's
amount is equal to 2/5 of B's amount, how much
amount does B have?
A) 484
B) 487
C) 520
D) 625
Q.12 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) 1000
B) 2200
C) 1500
D) 2000
Q.13
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) 1:2:3
C) 3:2:5
D) 2:3:5
Q.14 A mixture contains alcohol and water in the ratio
4 : 3. If 5 liters of water is added to the mixture, the
ratio becomes 4: 5. Find the quantity of alcohol in the
given mixture.
A) 10
B) 20
C) 15
D) None of these
What is Partnership ?
Important Concepts
Ratio of Divisions of Gains:
Suppose A and B invest Rs. x and
Rs. y respectively for a year in a business, then at
the end of the year:
(A's share of profit) : (B's share of profit) = x : y.
.
Suppose A invests Rs. x for p months and B invests
Rs. y for q months then,
(A's share of profit) : (B's share of profit)= xp : yq
Examples:
Q.1 A starts business with Rs. 3500 and after 5
months, B joins with A as his partner. After a year,
the profit is divided in the ratio 2 : 3. What is B's
contribution in the capital?
A) 8000
B) 9000
C) 7500
D) 8500
Q2. A, B, C subscribe Rs. 50,000 for a business. A
subscribes Rs. 4000 more than B and B Rs. 5000 more
than C. Out of a total profit of Rs. 35,000, A receives:
A.Rs. 8400
B.Rs. 11,900
C.Rs. 13,600
D.Rs. 14,700
Q3. A,B and C enter into a partnership investing Rs
35000, Rs 45000 and 55000. Find the their respective
shares in annual profit of 40,500
A) 10500, 13500, 19500
B) 10500, 13500, 18500
C) 10500, 13500, 17500
D) 10500, 13500, 16500
