Question

A number consists of two digits of which the tens digit exceeds the unit digit by 6. the number itself is equal to ten times the sum of the digits. find the number

Answer 1

let x and y be the digit in unit's place and ten's place of the number respectively

we have,
y = x + 6 --- (1)
the number = 10y+x
but the number = 10(x+y)
=> 10y+x = 10 (x+y)
=> 10(x+6)+x = 10x + 10 (x+6)
=> 10x + 60 + x = 10x + 10x + 60
=> -9x = 0
=> x = 0

putting x = 0 in (1)
y = 0+6 = 6

therefore the number = 10×6+0 = 60

Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

AnswEr:

• Required number will be 30.

Given:

• A number consists of two digit of which tens digit exceeds the unit digit by 3. The number is ten time sum of it's digit.

Need To Find:

• Required number will be = ?

ExPlanation:

Let the ten's digit be x.

And the unit's digit be y.

Therefore:

➠ Number = 10x + y

According to the first statement:

➠ Number = 10 × Sum of digits

➠ 10x + y = 10(x + y)

➠ 10x + y = 10x + 10y

➠ 10x - 10x = 10y - y

➠ 0 = 9y

Now, divide both terms by 9.

➠ y = 0

Hence:

• y = 0

______________________________________

According to the second statement:

➠ Ten's digit = 3 + Unit's digit

➠ x = 3 + y

➠ x = 3 + 0

➠ x = 3

Hence:

• x = 3

ThereFore:

• Required number will be 30.

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