Question 14

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

Solution:

Let "x y" be the required two digit number

x y = 4 (x + y)

Question 15

A two digit number such that the product of its digits is 21. When 36 is subtracted from the number the digits are interchanged. Find the number.

Solution:

Let "x y" be the required two digit number

A two digit number such that the product of its digits is 21

x(y) = 21

y = 21/x  ---- (1)

When 36 is subtracted from the number the digits are interchanged

x y - 36 = y x

10 x + y - 36 = 10 y + x

10 x - x + y - 10 y = 36

9 x - 9 y = 36

Now we are going to divide the whole equation by 9,so we get

x - y = 4  --- (2)

Now we are going to apply the value of y that is first equation in the second equation.

x - (21/x) = 4

x² - 21  = 4 x

x² - 4 x - 21 = 0

x² - 7 x + 3 x - 21 = 0

x (x - 7) + 3 (x - 7) = 0

(x - 7) (x + 3) = 0

x - 7 = 0             x + 3 = 0

x = 7                     x = -3

To get he value of y we have to apply 7 instead of x in the first equation

y = 21/x

y = 21/7

y = 3

Therefore the required two digit number is 73

Verification:

A two digit number such that the product of its digits is 21

7 (3) = 21

21 = 21

When 36 is subtracted from the number the digits are interchanged

73 - 36 = 37

37 = 37