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একটি মাকড়সা ভিন্ন ভিন্ন গতিতে যথাক্রমে হাঁটে ও দৌড়ায়। মাকড়সাটি ১০ সেকেন্ড হেঁটে এবং ৯ সেকেন্ড দৌড়ে ৮৫ মিটার দূরত্ব অতিক্রম করে। আবার ৩০ সেকেন্ড হেঁটে এবং ২ সেকেন্ড দৌড়ে ১৩০ মিটার দূরত্ব অতিক্রম করে। মাকড়সাটির হাঁটার ও দৌড়ের গতিবেগ কত?

হাঁটা ২ মি. /সে. দৌড় ২৫ মি./সে.

হাঁটা ৩ মি./সে. দৌড় ৬ মি./সে.

হাঁটা ৩ মি./সে. দৌড় ৬ মি./সে.

হাঁটা ৪ মি./সে. দৌড় ৫ মি./সে.

ANSWER : 4

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<p><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">মনেকরি,</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">একটি মাকড়সার হাঁটার গতিবেগ প্রতি সেকেন্ডে x মি.</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">এবং দৌড়ের গতিবেগ প্রতি সেকেন্ডে y মি.</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">১ম শর্তানুসারে,</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">10x  +  9y = 85 -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - (১)</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">২য় শর্তানুসারে,</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">30x  +  2y = 130 -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - (২)</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">১নং সমীকরণকে 3 দ্বারা এবং ২নং সমীকরণকে 1 দ্বারা গুণ করে পাই,</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">30x  +  27y = 255 -  -  -  -  -  -  -  -  -  -  -  -  -  - (3)</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">30x  +  2y = 130 -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  - (4)</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">৩নং সমীকরণ থেকে ৪নং সমীকরণ বিয়োগ করে পাই,</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">30x  +  27y - 30x - 2y = 255 - 130</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;"> = &gt; 25y = 125</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;"> = &gt; y = 125/25</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;"> = &gt; y = 5</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">১নং সমীকরণে y = 5 বসিয়ে পাই,</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">10x  +  9*5 = 85</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;"> = &gt;10x = 85 - 45</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;"> = &gt; x = 40/10</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;"> = &gt; x = 4</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">অতএব, মাকড়সাটির হাঁটার গতিবেগ  =  4মি./সে.</span><br style = "box - sizing: border - box; font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px;" /><span style = "font - family: 'source sans pro', 'helvetica neue', Helvetica, Arial, sans - serif; font - size: 15.73px; background - color: #ffffff;">এবং দৌড়ের গতিবেগ  = 5 মি./সে.</span></p>

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