Question

p:q =5:2 if p=a+b and q=a-b then find a:b

Answer 1

p/q =5/2,

(a+b)/(a-b) = 5/2,

2a+2b=5a-5b,

2b+5b=5a-2a,

7b=3a,


then

a/b=7/3

Answer 2

Ratio of p : q = 5 : 2 (given)

Form the first equation:

p = a + b (Given)

⇒ a + b = 5

⇒ a = 5 - b ------------------ [ 1 ]

Form the second equation:

q = a - b  (Given)

⇒ a - b = 2

⇒ a = b + 2  ------------------ [ 2 ]

Solve a and b:

[ 1 ] = [ 2 ] :

5 - b = b + 2

2b = 3

b = 3/2  ------------------  sub into [ 1 ]

a = 5 - b

a = 5 - 3/2 = 7/2

Find the ratio of a and b:

Ratio of a : b = 7/2 : 3/2

Multiply by 2:

Ratio of a : b = 7: 3

Answer: a : b = 7 : 3