Advertisements
Advertisements
Question
The denominator of a fraction exceeds Its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, we get `3/2`. Find the original fraction.
Advertisements
Solution
Let the numerator & denominator be ‘n’ & ‘d’
Given that denominator exceeds numerator by 8
∴ d = n + 8 ...(1)
If numerator increased by 17 & denominator decreased by 1,
it becomes (n + 17) & (d – 1), fraction is `3/2`
i.e `("n" + 17)/("d" - 1) = 3/2` by cross multiplying, we get
`("n" + 17)/("d" - 1) = 3/2`
2(n + 17) = 3(d – 1)
2n + 2 × 17 = 3d – 3
∴ 34 + 3 = 3d – 2n
∴ 3d – 2n = 37 ...(2)
Substituting equation (1) in (2), we get,
3 × (n + 8) – 2n = 37
3n + 3 × 8 – 2n = 37
∴ n = 37 – 24 = 13
d = n + 8 = 13 + 8 = 21
The fraction is `"n"/"d" = 13/21`
APPEARS IN
RELATED QUESTIONS
Divide the given polynomial by the given monomial.
8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2
Write the degree of each of the following polynomials.
2x + x2 − 8
Divide 6x3y2z2 by 3x2yz.
Divide 24a3b3 by −8ab.
Divide 5x3 − 15x2 + 25x by 5x.
Divide 4z3 + 6z2 − z by −\[\frac{1}{2}\]
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 15y4 − 16y3 + 9y2 −\[\frac{10}{3}\] y+6 | 3y − 2 |
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
3x2 + 4x + 5, x − 2
Divide: 8x − 10y + 6c by 2
