Advertisements
Advertisements
प्रश्न
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
Advertisements
उत्तर
Let the number of articles produced be x.
Therefore, cost of production of each article = Rs (2x + 3)
It is given that the total production is Rs 90.
∴ x(2x + 3) = 0
⇒ 2x2 + 3x − 90 = 0
⇒ 2x2 + 15x −12x − 90 = 0
⇒ x(2x + 15) −6(2x + 15) = 0
⇒ (2x + 15)(x − 6) = 0
Either 2x + 15 = 0 or x − 6 = 0
⇒ `x = (−15)/2` or x = 6
Since the number cannot be negative, therefore, x = 6.
So, the number of articles = 6
Cost of each article = 2 × 6 + 3 = Rs 15.
APPEARS IN
संबंधित प्रश्न
Solve for x : 12abx2 – (9a2 – 8b2 ) x – 6ab = 0
A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
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.
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
Factorise : m2 + 5m + 6.
Solve the following quadratic equations by factorization:\[\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3\]
If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
The number of quadratic equations having real roots and which do not change by squaring their roots is
Solve the following equation : x2 + 2ab = (2a + b)x
Solve the following equation: `x^2 + (a + 1/a)x + 1 = 0`
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
Solve equation using factorisation method:
(x + 3)2 – 4(x + 3) – 5 = 0
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
Find two consecutive even natural numbers such that the sum of their squares is 340.
The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.
Solve the following quadratic equation by factorization method.
3p2 + 8p + 5 = 0
Find the roots of the following quadratic equation by the factorisation method:
`3sqrt(2)x^2 - 5x - sqrt(2) = 0`
For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.
