Question

Some students planned a picnic. The budget for food was Rs. 480. But 8 of these failed t o go and thus cost of food for each member increased by Rs. 10. How many students attended the picnic ?

Answer 1

SOLUTION :  

Given : Budget for food =  ₹ 480

Let the number of students planned a picnic be x .

Share of each student = 480/x  

8 students failed to go to picnic , the remaining students = (x - 8)

New share for each student = 480/(x - 8)

480/(x - 8) = 480/x   +  10

480/(x - 8) -  480/x   =  10

480[1/(x - 8) - 1/x ] = 10

1/(x - 8) - 1/x  = 10/480

[x - (x - 8)] / x(x -8) = 1/48

[By taking LCM]

[x - x + 8)] / x² - 8x = 1/48

8/ x² - 8x = 1/48

x² - 8x = 8 × 48

x² - 8x = 384

x² - 8x -  384 = 0

x² + 16x - 24x - 384 = 0

[By middle term splitting]

x(x + 16) - 24(x + 16) = 0

(x - 24)(x + 16) = 0

(x - 24) = 0  or  (x + 16) = 0

x = 24  or x = - 16

Since, number of students can't be negative, so x ≠ - 16  

Therefore , x = 24

The number of students planned a picnic be  24.

Number of students attended the picnic = (x - 8) = 24 - 8 = 16  

Hence, the  number of students attended the  picnic be 16 .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Solution

Let number of students who planed to go for picnic be X

Amount given food expenses by students = Rs. 480

Therefore,

$amount given by one student = Rs. \frac{480}{x}$

But 8 students were not gone for picnic

Then, number of students who gone for picnic = (x - 8)

Now amount given by ( x - 8). Student = Rs. 480

According to question, 8 students were not gone to picnic, that's why rest student had to pay Rs. 10 more

$\frac{480}{x - 8} - \frac{480}{x} = 10$

$\frac{480x - 480(x - 8)}{x(x - 8)} = 10$

$480x - 480x + 3850 = 10( {x}^{2} - 8x)$

$10 {x}^{2} - 80x - 3840 = 0$

${x}^{2} - 8x - 384 = 0$

${x}^{2} - 24x + 16x - 384 = 0$

$x(x - 24) + 16(x - 24) = 0$

$(x - 24)(x + 16) = 0$

$x - 24 = 0 \: \: or \: \: x + 16 = 0$

$x = 24 \: \: or \: \: x = - 16$

Number of students cannot be negative.

X = 24

Therefore, number of students who gone for picnic

$= 24 - 8 = 16 \: \: \: \: \: answer$

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