Q) In a 2-digit number, the digit at the unit’s place is 5 less than the digit at the ten’s place. The product of the digits is 36. Find the number.

Ans: Let’s consider X is the digit at unit’s place and Y is the digit at ten’s place. The number will be 10 Y + X

By 1st given condition:  Y = X + 5  ………… (i)

Next, by 2nd given condition, product of the digits is 36

∴  X Y = 36

Substituting value of Y from equation (i), we get:

X Y = 36

∴ X (X + 5) = 36

∴ X + 5 X – 36 = 0

∴ X + 9 X – 4 X – 36 = 0

∴ X( X + 9) – 4( X + 9) = 0

∴ (X + 9) ( X – 4) = 0

∴ X = 4 and X = – 9

Here, we reject X = – 9 because it cannot be negative

Hence X = 4

from equation (i), Y = X + 5 = 9

Now, we get X = 4 and Y = 9

Therefore, the number is 10 Y + X = 9 x 10 + 4 = 94.

Therefore, the number is 94.

Check: 1) Difference of the digits is: 4 + 5 = 9

2) Product of the digits is: 9 x 4 = 36

Hence our solution is correct.

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