Subject
Quantitative Aptitude
Topic
Speed & Distance
A car starts running with the initial speed of 40 kmph, with its speed increasing every hour by 5 kmph. How many hours will it take to cover a distance of 385 km? (এক্টী কার 40 kmph আদিবেগে গতিশীল । প্রতি ঘন্টায় এর গতিবেগ 5 kmph করে বৃদ্ধি পায় তাহলে 385 km দূরত্ব অতিক্রম করতে কারটির কত সময় লাগবে?)
A car starts running with the initial speed of 40 kmph, with its speed increasing every hour by 5 kmph. How many hours will it take to cover a distance of 385 km? (এক্টী কার 40 kmph আদিবেগে গতিশীল । প্রতি ঘন্টায় এর গতিবেগ 5 kmph করে বৃদ্ধি পায় তাহলে 385 km দূরত্ব অতিক্রম করতে কারটির কত সময় লাগবে?)
ক)
7 hoursখ)
8(1/2)hoursগ)
9 hoursঘ)
9(1/2)hoursExplanation
ধরি, n ঘন্টায় উক্ত দূরত্ব অতিক্রম করে । তাহলে ১ম ঘন্টায় 40 km, ২য় ঘন্টায় 45 km, ৩য় ঘন্টায় 50 km....... এভাবে চলতে চলতে n তম ঘন্টায় 385 km দূরত্ব অতিক্রম করবে । অর্থাৎ, 40 + 45 + 50 + ......... n পর্যন্ত = 385 এখানে, প্রথম পদ a = 40, সাধারণ অন্তর d = 5 ধারার সমষ্টি, S n = (n/2){2a+(n-1)×d} = 385 => [(n/2){2×40 +(n-1)×d}] = 385 =>n{80+5n-5} = 385×2 => 80n + 5n 2 - 5n = 770 => n 2 + 15n - 154 = 0 [ 5 দ্বারা উভয় পক্ষকে ভাগ ] => n 2 + 22n - 7n - 154 = 0 => n(n+22) - 7(n+22) = 0 => (n+22)(n-7) = 0 ∴ n = -22 অথবা n = 7 সময় ঋণাত্বক হতে পারে না তাই n = 7 ∴ 7 ঘন্টা লাগবে ।Related questions
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