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.
                                                a * 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 b/b+a.

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.

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:b:c

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(0.08*0.18)

= square-root(8/100 * 18/100)

= square-root(144/10000)



Q. If x : y = 3 : 4, find (4x + 5y) : (5x - 2y)

A. 4x+5y : 5x-2y = 4(x/y)+5 / 5(x/y) - 2  we get this by dividing by y to both numerator and denominator.

substituting x/y in equation we can solve it.

Q.   Divide Rs. 600 in the ratio 4:2

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.


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