Question

If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2 the result is 2.if the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 9/7. Find the fraction

Answer 1

numerator = a

dinominator= b

 a x 4  = 2

 b - 2

4a = 2b - 4

2b = 4a + 4

b = 2a +2  ..............(1)

  a + 15     =  9  

   2b - 2           7

7a + 105   =  18b - 18   Apply (1)

7a + 105 = 18(2a +2) - 18

7a + 105 = 36a + 36 - 18

29a = 105 - 18

a = 87/29 = 3

b= 2a + 2 = 8

Fraction = 3/8

Answer 2

Step-by-step explanation:

Let the numerator of the required fraction be 'x' and the denominator be'y'. So, the required fraction would be x\y

According to the question,

Condition I,

If the numerator of a fraction is multiples by 4 and the denominator is reduced by 2, the result is 2

or,4x\y−2=2

or,4x=2(y−2)

or,x=2(y−2)\4

or,x=y−2\2 - (i)

Condition II,

If the numerator of the fraction is increased by 15 and 2 is subtracted from double of the denominator, the result is 9/7

or,x+15\2y−2=9\7

or,7(x+15)=9(2y−2)

or,7x+105=18y−18

or,7x+105+18=18y

or,7x+123=18y

or,7x=18y−123- (ii)

Put value of x from equation (i) in equation (ii), we get,

or,7(y−2) \ 2 = 18y−123

or,7(y−2)\2=18y−123

or,7y−14=2(18y−123)

or,7y−14=36y−246

or,246−14=36y−7y

or,232=29y

or,y=232\29

∴y=8

Put value of y in equation (i), we get,

or,x=8−2\2

or,x=6\2

∴x=3

So, (x,y) = (3,8)

Therefore, the required fraction is 3\8.