Hari takes a card from a deck which has got only two-digit numbers. The card he picked has got a number which can be obtained either by multiplying the digit sum by 8 and adding 1 to it or by multiplying the difference of digits by 13 and adding 2 to it. The number Hari got is ____.Marks : 2Negative Marks : 0Answer here54522541
Question
Hari takes a card from a deck which has got only two-digit numbers. The card he picked has got a number which can be obtained either by multiplying the digit sum by 8 and adding 1 to it or by multiplying the difference of digits by 13 and adding 2 to it. The number Hari got is ____.Marks : 2Negative Marks : 0Answer here54522541
Solution
The problem states that the number on the card can be obtained by either multiplying the sum of the digits by 8 and adding 1, or by multiplying the difference of the digits by 13 and adding 2.
Let's denote the tens digit as 'a' and the units digit as 'b'. So, the number on the card is 10a + b.
According to the first condition, 8(a+b) + 1 = 10a + b. Simplifying this equation, we get a = 7b + 1.
According to the second condition, 13|a-b| + 2 = 10a + b. Simplifying this equation, we get a = 13|a-b|/9 + 2/9.
Since a and b are digits, they must be integers from 0 to 9. By substituting possible values of b into the first equation, we find that a = 8 and b = 1 satisfy the equation.
Therefore, the number on the card that Hari picked is 81.
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