Question

The units digit of a two digit number exceeds the tens digit by 1 .If the product of

The digits is 25 less than the number , find the number. (let tens digit = x )​

Answer 1

67 is the number.

Step-by-step explanation:

Let the digit at tens place be x and y be the unit digit.

So,

The number = 10x + y

Given that,

Unit digit exceeds tens digit by 1. So,

y - x = 1

∵ y = x + 1

A.T.Q.

(x) * (x + 1) = (10x + y) - 25

x^2 + x = (10x + y) - 25

by putting the value of y in the above equation,

x^2 + x = (10x + (x + 1) - 25

x^2 + x = (11x + 1) - 25

x^2 + x - 11x = -24

x^2 - 10x = -24

x^2 - 10x + 24 = 0

= x^2 - 4x - 6x + 24

= x(x - 4) -6(x - 4)

= (x - 6) (x - 4)

Thus, x = 6 or x = 4. Let's see which one applies.

Taking x = 6

so, by putting the value in 10x + y

= 10(6) + (6 + 1)

= 60 + 7

= 67

We know that the product is less than 25 by the number. so,

6 * 7 = 42

since 67 - 42 = 25

Thus, 67 is the number.

Learn more: Find the number

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