InterviewSolution
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InterviewSolution
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A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number. |
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Answer» Let the two-digit number = 10x + y Case I Multiplying the sum of the digits by 8 and then subtracting 5 = two-digit number `rArr " " 8xx(x+y)-5=10x+y` `rArr " " 8x+8y-5=10x+y` `rArr " " 2x-7y=-5 " " ...(i)` Case II Multiplying the difference of the digits by 16 and then adding 3 = two-digit number `rArr " " 16xx(x-y)+3=10x+y` `rArr " " 16x-16y+3=10x+y` `rArr " " 6x-17y=-3 " " ...(ii)` Now, multiplying in Eq. (i) by 3 and then subtracting from Eq. (ii), we get `{:(6x-17y=-3),(ul(underset(-)6x+underset(+)21y=underset(+)-15)),(4y=12rArry=3):}` Now, put the value of y in Eq. (i), we get `2x-7xx3=-5` `rArr 2x=21-5=16 rArr x=8` Hence, the required two-digit number `=10x+y` `=10xx8+380+3=83` |
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