Question

A student was given a task to multiply the number 78 by the two-digit number with the tens digit by 4 greater than the ones digit . Accidentally, she reversed the digits of the second factor and the product was 2808 smaller than the correct product. What is the correct second factor?​

Answer 1

78(50x+1x)-78(10x+5x)=2808
51x-15x=36
36x=36
X=1

Therefore the number is 50x+1x=51

Answer 2

Given: A student was given a task to multiply the number 78 by the two-digit number with the tens digit by 4 greater than the ones digit. Accidentally, she reversed the digits of the second factor and the product was 2808 smaller than the correct product.

To find: The correct second factor.

Solution:

• Let the digits of the second factor be x and y. So, the second factor can be represented as,

        $10x + y$

• When the digits of the second factor are reversed it can be represented as,

        $10y + x$

• According to the question, the reversed digits multiplied by 78 give 2808.

        $(10y+x) * 78 = 2808$

        $(10y+x) = 36$

• So, the second factor is obtained by reversing the digits of 36, that is, 63.

Therefore, the correct second factor is 63.