Solve the following Mathematical Problems :

After traveling 108 km, a cyclist observed that he would have required 3 hours less if he could have traveled at a speed 3 km/hr more. At what speed did he travel?

Created: 5 months ago | Updated: 5 days ago

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প্রশ্নে বলা হচ্ছে যে, 108 কিলোমিটার যাওয়ার পরে একজন সাইকেল আরোহী বুঝতে পারলেন যে তিনি যদি 3 km/hr বেশি বেগে যেতেন, তবে তার 3 ঘণ্টা কম সময় লাগতো। সাইকেল আরোহীর গতিবেগ কত ?

$L e t, t h e s p e e d b e x k m / h r . S i n c e d i s \tan c e i s 108 k m, t i m e = \frac{108}{x} h r s W h e n s p e e d i s i n c r e a s e d b y 3 k m / h r, s p e e d i s = (x + 3) k m / h r ∴ T h e r e q u i r e d t i m e = \frac{108}{x + 3} h r s A c c o r d i n g t o t h e q u e s t i o n, \frac{108}{x} - \frac{108}{x + 3} = 3 \Rightarrow \frac{108 (x + 3) - 108 x}{x (x + 3)} = 3 \Rightarrow \frac{108 x + 324 - 108 x}{x^{2} + 3 x} \Rightarrow 324 = 3 x^{2} - 9 x \Rightarrow 324 - 3 x^{2} - 9 x = 0 \Rightarrow - 3 x^{2} - 9 x + 324 = 0 \Rightarrow - 3 (x^{2} + 3 x - 108) = 0 \Rightarrow x^{2} + 3 x - 108 = 0 \Rightarrow x^{2} + 12 x - 9 x - 108 = 0 \Rightarrow x (x + 12) - 9 (x + 12) \Rightarrow (x + 12) (x - 9) = 0 S o e i t h e r, x - 9 = 0 o r, x + 12 = 0 i f, x + 12 = 0 t h e n, x = - 12 ∴ T h e s p e e d 9 k m [S i n c e v e l o c i t y x \neq - 12] H e t r a v e l e d a t a s p e e d o f 9 k m / h r . (a n s)$

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if m=7- $4 \sqrt{3}$ ,then find the value of $\sqrt{m} + \frac{1}{\sqrt{3}}$

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Solve the following Mathematical Problems

A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?

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Solve the following Mathematical Problems

In a cricket match, Team A scored 232 runs without losing a wicket. The score consisted of eves, wised and runs scored by two opening batsmen: Rick and Stew. The runs scored by the two batsmen are 26 times wide. There are 8 more byes than wide. If the ratio of the runs scored by Rick and Stew is 6 : 7, what were the runs scored by Rick?

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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: 5 months ago | Updated: 5 days ago

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Solve the following Mathematical Problems