Advertisements
Advertisements
Question
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?
Advertisements
Solution
Let the length of the piece be x metres.
Then, rate per metre = `35/x`
According to question, new length = (x + 4) meters.
Since the cost remain same. Therefore, new rate per metre `=35/(x+4)`
It is given that
`35/x+35/(x+4)=1`
`(35(x+4)-35x)/(x(x+4))=1`
`(35x+140-35x)/(x^2+4x)=1`
`140/(x^2+4x)=1`
140 = x2 + 4x
x2 + 4x − 140 = 0
x2 + 14x − 10x − 140 = 0
x(x + 14) − 10(x + 14) = 0
(x + 14) (x − 10) = 0
x + 14 = 0
x = −14
Or
x − 10 = 0
x = 10
Because x cannot be negative.
Thus, x = 10 is the require solution.
Therefore, the length of the piece be x = 10 meters.
RELATED QUESTIONS
Solve the following quadratic equation for x:
`x^2+(a/(a+b)+(a+b)/a)x+1=0`
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Solve the following quadratic equations by factorization:
9x2 − 3x − 2 = 0
The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.
A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
Solve the following quadratic equation by
factorisation.
5m2 = 22m + 15
The sum of two natural numbers is 20 while their difference is 4. Find the numbers.
Find the value of k for which the following equations have real and equal roots:
\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Solve the following equation: `1/("x" - 1) + 2/("x" - 1) = 6/"x" , (x ≠ 0)`
Solve the following equation: abx2 +(b2-ac) x - bc = 0
Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.
The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
Solve equation using factorisation method:
4(2x – 3)2 – (2x – 3) – 14 = 0
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3x + 2 = 0; x = 2, x = -1
Solve the following equation by factorization
x(6x – 1) = 35
Solve the following equation by factorization
(x – 4)2 + 52 = 132
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
Find the roots of the following quadratic equation by the factorisation method:
`21x^2 - 2x + 1/21 = 0`
The roots of the equation x2 + 3x – 10 = 0 are ______.
(x – 3) (x + 5) = 0 gives x equal to ______.
If x4 – 5x2 + 4 = 0; the values of x are ______.
