Solve the following Mathematical Problems

A group of students hired a bus for TK. 3000 for going to a picnic. They had an understanding that each participant would share the charge is equal amounts. But because of 10 students were not turning up, the charge per student increased by TK. 10 over the initial estimate. What was the number of students who originally registered for the picnic?

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

প্রশ্নে বলা হচ্ছে যে, Picnic এ যাবার জন্য কয়েকজন ছাত্র 3,000 টাকায় একটি বাস ভাড়া করল। তারা প্রত্যেকে সমান ভাড়া দেবার জন্য একমত হলো। কিন্তু 10 জন ছাত্র না আসায় মাথাপিছু ভাড়া 10 টাকা বেড়ে গেল। প্রথমে কতজন ছাত্র Picnic এ যাবার কথা ছিল ?

Suppose, the number of students were x

Per head amounts= $\frac{3000}{x}$ TK.

As 10 students did not turn up then charged amount will be $\frac{3000}{x - 10} T k$

$∴ P e r h e a d a m o u n t s = T K . \frac{3000}{x - 10} A c c o r d i n g t o t h e q u e s t i o n \frac{3000}{x - 10} - \frac{3000}{x} = 10 \Rightarrow \frac{3000 x - 3000 x + 3000}{(x - 10) x} \Rightarrow \frac{30000}{x^{2} - 10 x} = 10 \Rightarrow 10 x^{2} - 100 x = 30, 000 \Rightarrow 10 x^{2} - 100 x - 30, 000 = 0 \Rightarrow x^{2} - 10 x - 30, 000 = 0 \Rightarrow x (x - 60) + 50 x - 3000 = 0 \Rightarrow x (x - 60) + 50 (x - 60) \Rightarrow (x + 50) (x - 60) = 0 \Rightarrow x - 60 = 0 ∴ x = 60$