Question

1) The tens digit of a two number is less by 3 than the unit digit. If the product of the two digits are subtracted from the number, the result is 15. Let us write the unit digit of the number by calculation.​

Answer 1

Question :- The tens digit of a two number is less by 3 than the unit digit. If the product of the two digits are subtracted from the number, the result is 15. Let us write the unit digit of the number by calculation.

Solution :-

Let us assume that, the required two digits number is (10x + y) where y is the unit digit number and x is ten's digit number.

so,

→ unit digit - ten's digit = 3

→ y - x = 3

→ y = (3 + x)--------- Eqn.(1)

also,

→ (10x + y) - xy = 15

putting value of y from Eqn.(1),

→ 10x + 3 + x - x(3 + x) = 15

→ 11x + 3 - 3x - x² = 15

→ x² - 8x + 12 = 0

→ x² - 6x - 2x + 12 = 0

→ x(x - 6) - 2(x - 6) = 0

→ (x - 6)(x - 2) = 0

→ x = 2 or 6.

therefore,

• if x = 2 => y = 3 + x = 5 .
• if x = 6 => y = 3 + x = 9 .

Hence, the unit digits of the number will be either 5 or 9.

Answer 2

Answer:

Given :-

• The tens digit of a two number is less by 3 then the unit. If the product of the two digits are subtracted from the number, the result is 15. Let us write the unit digit of the number by calculator.

Find Out :-

• The unit digit.

Solution :-

Let the unit digit be 'x'

So, the tens digit is 'x - 3 '

Then, the whole number,

➻ 10(x - 3 ) + x

➻ 10x - 30 + x

➻ 10x + x - 30

➭ 11x - 30

Now, according to the question,

➻ 11x - 30 - x(x - 3) = 15

➻ 11x - 30 - x² + 3x = 15

➻ 11x + 3x - 30 - x² = 15

➻ 14x - 30 - x² = 15

➻ - x² + 14x - 30 - 15 = 0

➻ - x² + 14x - 45 = 0

➻ x² - 14x + 45 = 0

➻ x² - (5 + 9)x + 45 = 0

➻ x² - 5x - 9x + 45 = 0

➻ x(x - 5) - 9(x - 5) = 0

➻ x - 9 = 0 , x - 5 = 0

➻ x = 9

➠ Either,

➻ x = 5

∴ The units are 9 or 5.