class 10
lesson: pair of linear equation in two variable
Answers
Answer:
The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.
Solution:
Let’s assume the numerator of the fraction to be x and the denominator of the fraction to be y.
So, the required fraction is x/y.
From the question it’s given as,
The numerator of the fraction is 4 less the denominator.
Thus, the equation so formed is,
x = y – 4
⇒ x – y = −4 …… (i)
And also it’s given in the question as,
If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is 8 times the numerator.
Putting the above condition in an equation, we get
y + 1 = 8(x-2)
⇒ y + 1 = 8x–16
⇒ 8x – y = 1 + 16
⇒ 8x – y = 17 …… (ii)
Solving (i) and (ii),
Subtracting the equation (ii) from (i), we get
(x – y) – (8x – y) = – 4 – 17
⇒ x – y − 8x + y = −21
⇒ −7x = −21
⇒ x = 21/7
⇒ x = 3
Substituting the value of x =3 in the equation (i), we find y
3 – y = – 4
⇒ y = 3+4
⇒ y = 7
Therefore, the fraction is 3/7.