Q5 of 54 Page 77

A two digit number is four times the sum and three times the product of its digit. Find the number.

A two-digit numbers can be expressed as where x is the tens digit and y is the ones digit. For example:

According to the question,


Two-digit number is equal to four times the sum of its digit 10x + y = 4 (x + y)


10x + y = 4x + 4y


10x – 4x = 4y – y


6x = 3y



2x = y ……(1)


Number is three times the product of the digit.


10x + y = 3 (x × y)


From (1) y = 2x


10x + 2x = 3(x × 2x)




X = 2


Put x = 2 in (1)


2×2 = y


Y = 4


Therefore, tens digit = x = 2, ones digit = y = 4 .Therefore, the number is 24.


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