Advertisements
Advertisements
Question
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
Advertisements
Solution
Let x students planned a picnic.
Then, the share of each student `= 500/x`
According to question, 5 students fail to go picnic, then remaining students = (x - 5).
Therefore, new share of each student `500/(x-5)`
It is given that
`500/(x-5)-500/x=5`
`(500x-500x+2500)/((x-5)x)=5`
`2500/(x^2-5x)=5`
2500 = 5(x2 - 5x)
`2500/5=x^2-5x`
500 = x2 - 5x
x2 - 5x - 500 = 0
x2 + 20x - 25x - 500 = 0
x(x + 20) - 25(x + 20) = 0
(x + 20)(x - 25) = 0
x + 20 = 0
x = -20
Or
x - 25 = 0
x = 25
Because x cannot be negative.
Thus, the total numbers of students attend a picnic
= x - 5
= 25 - 5
= 20
Therefore, the total numbers of students attend a picnic be x = 20.
RELATED QUESTIONS
Solve the following quadratic equation by factorization method : `x^2-5x+6=0`
Solve the following quadratic equation by factorization method: 9x2-25 = 0
Solve the following quadratic equation for x: x2 – 2ax – (4b2 – a2) = 0
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.
Solve the following quadratic equations by factorization:
`2/2^2-5/x+2=0`
Solve the following quadratic equations by factorization:
a2x2 - 3abx + 2b2 = 0
Solve the following quadratic equations by factorization:
`(x+3)/(x-2)-(1-x)/x=17/4`
Solve the following quadratic equations by factorization:
`7x + 3/x=35 3/5`
Divide 29 into two parts so that the sum of the squares of the parts is 425.
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
`3x^2-x-2=0`
Solve the following quadratic equation by factorisation.
2m (m − 24) = 50
Solve the following quadratic equations by factorization:
\[9 x^2 - 6 b^2 x - \left( a^4 - b^4 \right) = 0\]
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
The number of quadratic equations having real roots and which do not change by squaring their roots is
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Find two consecutive natural numbers such that the sum of their squares is 61.
A wire ; 112 cm long is bent to form a right angled triangle. If the hypotenuse is 50 cm long, find the area of the triangle.
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
Which of the following are the roots of the quadratic equation, x2 – 9x + 20 = 0 by factorisation?
