A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 2.7 more than the previous one. What was the difference of the two digits a and b?Options863None of these
Question
A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 2.7 more than the previous one. What was the difference of the two digits a and b?Options863None of these
Solution
The difference between the two digits a and b can be found by following these steps:
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The average of 10 numbers increased by 2.7 when one number was mistakenly switched from 'ba' to 'ab'. This means the sum of the numbers increased by 27 (because 2.7 * 10 = 27).
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The number 'ba' is equal to 10b + a and the number 'ab' is equal to 10a + b. The difference between 'ab' and 'ba' is therefore 9a - 9b.
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Since the sum of the numbers increased by 27 when 'ba' was switched to 'ab', we can set up the equation 9a - 9b = 27.
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Simplifying this equation gives a - b = 3.
So, the difference between the two digits a and b is 3.
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