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some students planned a picnic. the total budget for food was rs 2000. due to confusion 5 students failed to attend the picnic and thus the cost of food for each member increased by rs 20. how many students attended the picnic and how much each student paid for food

some students planned a picnic. the total budget for food was rs 2000. due to confusion 5 students failed to attend the picnic and thus the cost of food for each member increased by rs 20. how many students attended the picnic and how much each student paid for food

Grade:Select Grade

8 Answers

pracheesh singh
26 Points
9 years ago

initial budget=2000

initial no. of students= x

final no. of students= x-5

intial money given by each student= y

final money given by each student= y+20

so equation will be,

xy=2000 ..........(1)

(x-5)(y+20)=2000..................(2)

(x-5)(2000+20x)/x=2000

2000x-10000+20x^2-100x=2000x

20x^2-100x-10000=0

x^2-5x-500=0........(4)

Find x=?

then the rest procedure is very simple!!!!!!!!!!

Thankyou!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11111111

rohit yadav
34 Points
9 years ago

5 student attend the picnic . 200 rupees each student paid .

Akash Kumar Dutta
98 Points
9 years ago

please post some tough questions next time.

Abhishekh kumar sharma
34 Points
9 years ago

we have let x= no of student

y=money by each

then, xy=2000

and also , (x-5)(y+20)=2000

on simplifying we get

xy+20x-5y-100=xy

putting y=2000/x

we get  x^2-5x-500=0

then x=25 or -20

since -20 cannot be the no of student so x=25

Ankan Mukherjee
18 Points
9 years ago

20 students attended the picnic

each paid rs 100

ashwen venkatesh
19 Points
9 years ago

let the no of students be ''x''

let the amount spent be ''y''

according to question,

x.y=2000   ..............(1)

since five students failed to attend =(x-5)

since the cost increased by rs.20=(y+20)

now the equation (1) becomes

(x-5)(y+20)=2000

xy+20x-5y-100=2000

20x-5y-100=0    [from (1)]

dividing throughout by 5,we get

4x-y-20=0

substitute the value of y from equation (1), i.e.,  y=2000/x

you will get equation like this

x.x-5x-500=0

when u solve this u wil get,x=25.

and final answer is 25 students attended the picnic

A
11 Points
6 years ago
Let total no. of students=x                           budget for one student=Rs 2000                          now 5 students failed to go so cost for each member increased by Rs20 .                so cost for one student=Rs2000÷x-5.                A.T.Q                                                                 (2000÷x-5) -(2000÷x)=20                             2000(x-x+5÷x2-5x)=20                                     500=x2-5x      ,x2-5x-500=0                               x(x-25)+20(x-25)                                                  (x-25) (x+20)                                                   x=25 & x=-20                                                   no.of students =25(rejecting -ve value
Yash Chourasiya
askIITians Faculty 256 Points
2 years ago
Dear Student

Let x be the number of students who planned a picnic.
Original cost of food for each member = Rs. 2000/x
Five students failed to attend the picnic. So, (x-5)students attended the picnic.
New cost of food for each member = Rs. 2000/(x-5)
According of the given condition
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I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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