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A survey of n people in the town of X found that 50% of them prefer Brand A. Another survey of 100 people in the town of Y found that 60% prefer Brand A. In total, 55% of all the people surveyed together prefer Brand A. What is the total number of people surveyed?

A survey of n people in the town of X found that 50% of them prefer Brand A. Another survey of 100 people in the town of Y found that 60% prefer Brand A. In total, 55% of all the people surveyed together prefer Brand A. What is the total number of people surveyed? Correct Answer 200

প্রশ্নমতে, x শহরে Brand A পছন্দ করে 50% of n = 50/100×n = n/2 এবং, Y শহরে Brand A পছন্দ করে 60% of 100 = 60 জরিপে অংশগ্রহণকারী মোট people এর সংখ্যা ( n + 100) জন। প্রশ্নমতে, (n/2 + 60)/ ( n + 100) ×100 = 55 n/2 + 60 = 55/100 ( n + 100) (n + 120)/2 = ( 11n + 1100)/20 20n = 2400 = 22n = 2200 2n = 200 n = 100 সুতরাং, মোট জরিপকৃত people সংখ্যা = ( n + 100) = ( 100 + 100) = 200

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