Q. 64.5( 267 Votes )
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.
To find: Number of articles produced and cost of each article.
Let the number of articles produced be x.
Therefore, cost of production of each article = Rs (2x + 3)The total cost of production = Total quantity produced x cost of one article
It is given that the total cost of production is Rs 90.
∴ x (2x + 3) = 90⇒ 2x2 + 3x = 90
⇒ 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,
i.e., x = or x = 6
As the number of articles produced can only be a positive integer,
Therefore, x can only be 6.
Hence, the number of articles produced = 6
Cost of each article = 2 × 6 + 3
= 12 + 3
= Rs 15
Rate this question :
The area of a right angled triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 m.RD Sharma - Mathematics
Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm2. Find the sides of the squares.RD Sharma - Mathematics
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.RD Sharma - Mathematics
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.RD Sharma - Mathematics
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express trains is 11 km / hr more than that of the passenger train, find the average speeds of the two trains.RD Sharma - Mathematics
While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes to reach the destination, 1500 km away in time, the pilot increased the speed by 100 km / hr. Find the original speed / hour of the plane.RD Sharma - Mathematics
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?RD Sharma - Mathematics
The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is , find the original fraction.RD Sharma - Mathematics
The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.RD Sharma - Mathematics