Chapter 8: RATIO AND PROPORTION
Ratio means two quantities in the same units like Hari's
height is 100 cm and Ram's height is 200 cm so the ratio of
their heights is 100/200 or 1:2. the ratio has no units.
Proportion is equality of two ratio's a:b = c:d we write as
a:b::c:d and a,d are extremes and b,c are means. The product
of means = product of extremes.
* d = b * c
When we have to divide a quantity 'x' into a:b we
need to break it into two parts one is a/a+b and second is
Componendo - Dividendo rule:
if a:b = c:d then (a+b)/(a-b) = (c+d)/(c-d)
If x ∝ y i.e. x is directly
proportional to y which means when x increases y too
increases and when x decreases y to decreases.
If x ∝ 1/y i.e. x
is inversely proportional to y which means if x increases y
decreases and when x decreases y increases.
|x ∝ y then x =
k*y where k = constant
|x ∝ 1/ y then x
* y= k where k = constant
Questions & Answers:
Q. If a:b = 3:4 and b:c is 5:4 then find
A. The value common to both is b so b has
to made same in both ratios. The LCM of 4,5 is 20 so we
convert the ratios by multiplication
a:b = (3*5):(4*5) and b:c = (5*4)/(4*4)
a:b = 15:20 and b:c = 20:16 now b value is same in both
sides and so we can merge on basis of 'b'.
a:b:c = 15:20:16
Q.Find fourth proportional between 4,9,12
A. Assume fourth proportional as 'x'. so
we get 4:9::12:x .
As we know from above formula: 4*x = 9*12 so we can get
value of x.
Q. Third proportional to 16, 36.
A. Assume third proportional is 'x'. so
we get 16:36::36:x
As we know from formula that 16*x = 36*36 we can get 'x'.
Q. Mean proportional between 0.08 and 0.18
A. mean proportional =
= square-root(8/100 * 18/100)
Q. If x : y = 3 : 4, find (4x + 5y) : (5x
A. 4x+5y : 5x-2y = 4(x/y)+5 / 5(x/y) -
2 we get this by dividing by y to both numerator and
substituting x/y in equation we can solve it.
Q. Divide Rs. 600 in the ratio
A. the ratio 4:2 means first value shall
be 4/4+2 and second value shall be 2/4+2 i.e. 600 has to be
divided into 4/6 and 2/6 parts. so we get 400,200.
Q. A bag contains 50 p, 25 P and 10 p
coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the
number of coins of each type.
A. Since ratio is 5:9:4 this means actual
number of coins can be 5x, 9x and 4x.
We know that, 5x*(1/2) + 9x*(1/4) + 4x*(1/10) = 206 as we
converted the paisa values to rupee.
Q. A mixture contains alcohol and
water in the ratio 4 :
3. If 5 litres of water is added
to the mixture, the ratio becomes 4: 5. Find the
quantity of alcohol in the given mixture.
A. Alcohol and water were 4x and 3x and
now 4x / 3x+5 = 4 / 5.
Score more than 80% marks and move ahead else stay back and read again!