Question

The product of two positive numbers a and b is 240. if twice of b is more than a by 4, then b is

Answer 1

a×b=240
Therefore, a=240/b------i)
2b=a+4
Therefore, a=2b-4------ii)
From equations i) and ii),
240/b= 2b-4
2b²-4b = 240
b²-2b = 120
b²-2b-120=0
Solve the equation to get the value of b, and then in equation i) or ii), substitute the value of b to obtain the value of a.

Answer 2

Given :- ab = 240 ....( i )

• 2b + 4 = a ....( ii )

Putting in ( i ) from ( ii )

ab = 240

( 2b + 4 ) b = 240

2b² + 4b - 240 = 0

b² + 2b - 120 = 0

b² + 12b - 10b - 120 = 0

b ( b + 12 ) - 10 ( b + 12 ) = 0

( b - 10 ) ( b + 12 ) = 0

• ( b - 10 ) = 0
b = 10

• ( b + 12 ) = 0
b = - 12 ......( given in the question that the no. are positive so , it is neglected )

So, b = 10