Ratio & Proportion
Ratio:- The comparative relation between two quantities of same type is called ratio.
If the two quantities are a and b, then ratio of a and b is represented as
a/b = a:b
Notes:- Two quantities can be compared only if they are in the same unit.
E.g.:- Kg : Kg
Hour : Hour
Min : Min
In ratio 1st number in ‘x’ is called “antecedent” and second number in ‘y’ is called ‘consequent.”
when we multiply or divide antecedent and consequent of the ratio by a same non-zero number, it does not change the ratio.
E.g.:- a:b = a/b = (a*c)/(b*c) = ac : bc = a:b
Proportion:- Proportion refers to the equality of two ratios.
Two equivalent ratios are always in proportion.
Proportion are denoted by the symbol (::).
These are two types of to proportions.
1. Direct proportion
2.Inverse propontim
Direct proportion: Direct proportion describes the direct relationship between two quantities. If one quantity increases, the other quantity also increases and vice versa.
e.g. if the speed of car is increased, then it Covers more distance in a fixed period of time.
2.Inverse proportion: Inverse proportion describes the relationship between two quantities in which if one quantity increases, the other quantity decreases and vice- Versa.
Law of Ratios
a/b = c/d then
ad = bc
a/c = b/d
(a+b)/b = (c+d)/d
(a+b)/b = (c+d)/d
(a+b)/b = (c+d)/d
- Q1. If A: B=2:3 and B:C = 5:3, then A:B:C = ?
(a) 10:15:9 (b) 15:10:9
(c) 9:10:11 (d)11:12:10
Solution: (a)
A:B B : C
1 : 2 2 : 3
A:B:C
1:2:3 - Q2. If 2A=3B and 4B=5C, then A:C=?
(a) 3:5 (b) 8:15
(c) 15:8 (d) 4:3
Solution: (c)
2A =3B 4B=5C
A/B=3/2 B/C=5/4
A : B B : C
(3:2)_(×5) (5∶4)_(×2)
A : B : C
15 : 10 : 8
A : C
15 : 8
- Q3. Rs. 10000 are divided among three workers in the ratio 2:3:5. The share of second worker is:
(a) 2560 (b) 3000
(c) 3200 (d) 3840
Solution: (b)
2:3:5
3/10×10000=3000 - Q4. If a number is multiplied by three-fourth of itself, the value thus obtained is 10800. What is that number?
(a) 210 (b) 180 (c) 120
(d) 160 (e) 140
Solution: (c)
x×3/4 x=10800
x=120
- Q5. The ratio of boys and girls in a school is 3:2. When 6 more girls join this ratio becomes 6:7. How many boys are there in the school?
(a) 24 (b) 30
(c) 42 (d) 12
Solution: (d)
3x/(2x+6)=6/7
21x=12x+36
9x=36
X=4
3x=12
- Q6. The monthly incomes of A and B are in the ratio 2:3 and their monthly expenses are in the ratio 5:9. If each of them saves Rs. 600 per month then their monthly incomes are:
(a) Rs.1500, Rs.2250 (b) Rs.1200 Rs. 1800
(c) Rs. 1600, Rs. 2400 (d) Rs. 1400, Rs. 2100
Solution: (c)
(2x-600)/(3x-600)=5/9
X=600
2x=1200
3x=1800
