Q.

Find two-digit number the quotient of whose division by the product of its digits is equal to 83 and the difference between the required number and the number consisting of the same digits written in the reverse order is 18.


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a

65

b

63

c

64

d

62 

answer is C.

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Detailed Solution

Let n(a,b) be two digit number.
n(a,b) = 10a+b
Given, n(a,b)ab=83
Or, 10a+bab=83
Given that   n(a,b)−n(b,a)= 18
9(a−b)= 18
Or, a−b = 2
Or, a = b+2
30a+3(a−2) = 8a(a−2)
33a−6 = 8a2−16a
8a2−49a+6= 0
(8a−1)(a−6)= 0
Then, a = 6, a 18
b = a−2 = 4
The original number = 10a + b
                                  = 10(6) + 4
                                  = 64
64 is the required number.
 
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