QUADRATIC EQUATIONS
A person on tour has Rs. 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down
his daily expenses by Rs. 3. Find the original duration of the tour.
15. Some students planned a picnic. The budget for the food was Rs. 480. But, eight of the students failed
to go and thus the cost of food for each member increased by Rs. 10. How many students attended the
pienie?
16. A piece of cloth costs Rs. 35. If the piece were 4 metres longer and each metre costs Re. 1 less, the cost
would remain unchanged. How long is the piece ?
17. In a class test, the sum of Radhika's marks in Mathematics and English is 30. Had she got 2 marks
more in Mathematics and 3 marks less in English, the product of their marks would have been 210.
(CBSE 2014, 121
Find her marks in two subjects.
18. 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
Answers
Answer for 1st question
For X days he had ₹360
If the tour extended by 4 days the daily expenses are cut by ₹ 3
Thus no of days = X + 4
Daily expense = 360/X
New daily expense would be = 360/(X+4)
Difference would be = ₹3
3 = 360/X - 360/(X+4)
3 = [360(X+4) - 360X]/ [X(X+4)]
3 = (360X + 1440 - 360X)/ (X² + 4X)
3 = 1440/ (X²+ 4X)
3(X² + 4X) = 1440
X²+ 4X = 1440/3
X² + 4X = 480
X²+ 4X - 480 = 0
X² + 24X - 20X - 480 = 0
X(X+24) - 20(X+24) = 0
(X-20)(X+24) = 0
X = 20 or X = -24
Since number of days cannot be negative thus,
No of days = 20
Answer for question no15
Let the no of students be x
let the cost of each student be y
so x.y = 480 ⇒ y = 480/x
so 8 students failed to go , so cost of each food increased by 10
(x-8)(y+10)=480
(x-8)(480/x+10)=480
x² - 8x - 384 = 0
x² + 16x - 24x - 320 = 0
(x - 24)(x + 16) = 0
so x = - 16 or 24
number of students cannot be negative .Therefore 24 students arrived to picnic
Answer for question 16
Let the length of the cloth be 'x' metres
therefore,
cost of 1 m cloth = 35/x
now,
(35/x) -1 =35/x+4
35/x - (35/x+4) = 1
35x+140-35x/x(x+4) = 1
140 =x2+4x
x2 +4x-140 =0
by factorization method
x²+4x-140=0
x²+14x-10x-140=0
x(x+14)-10(x+14)=0
(x+14)(x-10)=0
x=-14orx=10
length cannot be negative
Therefore answer is 10 m
17
Let radhika's mark in maths exam be x
Given that sum of radhikas mark in English and maths is 30
Marks in maths + marks in English =30
x+marks in English =30=30-x
Also it is given that she had got two mark more in maths and 3 marks less in English the product of their marks would have been to 210
(marks in maths +2)(marks in english-3)=210
(x+2)(27-3)=210
x(27-x)+2(27-x)=210
27-x²+54-2x=210
27x-x²+54-2x-210=0
-x²-2x+27x+54-210=0
-x2+25x-156=0
x²-25x+156=0
x²-12x-13x+156=0
x(x-12)-13(x-12)=0
x=12or x=13
case 1
mark in maths is x= 12
english mark= 30-12=18 marks
case2 marks in math =13
English mark = 30-x= 30-13=17marks
I think last question is in ncert textbook examples please refer it