Question

The digit at unit place of a two digit number is1 more than the digit at ten's place if the number is three more than five times of the sum of the digit find the number

Answer 1

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$\underline{\underline{\huge{\textbf{Solution}}}}$

Given,
For a two digit Number,
Unit's Digit = Ten's Digit + 1 ---------[1]
No. = 5(sum of it's digits) + 3--------[2]

$\underline{\lage{\textbf{Step-1:}}}$
Express the Unit's Digit and ten's digit of the Number in terms of one Variable using relation given in [1]

Let Ten's Digit of the two digit number be x
$\implies$Unit's Digit of the two digit Number = x+1

$\underline{\large{\textbf{Step-2:}}}$
Find the Sum of digits of the Number

Sum of Digits of two digit Number = Ten's place Digit + Unit's place Digit.

$\implies$Sum of Digits = x+(x+1) = 2x+1

$\underline{\large{\textbf{Step-3:}}}$
Express the two digit Number in terms of the variable considered.

A Number is equal to sum of product of weight of the digit at each place and Face value at that place.

Two Digit No. = 10(Ten's place Digit) + 1(Unit's place Digit)

Two digit No. = 10(x)+1(x+1) = 11x+1

$\implies$ Two digit No. = 11x+1 ------[3]

$\underline{\large{\textbf{Step-4:}}}$
Find the value of Ten's place Digit (variable considered) using the relation given by [2].

Substituting Values

$\implies 11x+1 = 5(2x+1)+3$
$\implies 11x+1 = 10x+5+3$
$\implies 11x+1 = 10x+8$
$\implies 11x-10x = 8-1$
$\implies x = 7$.

$\underline{\large{\textbf{Step-5:}}}$
Find the value of Unit's place Digit using the relation given by [1].

Substituting Values

$\implies Ten's\: digit = 7+1= 8$
$\implies Ten's\: digit = 8$

$\underline{\large{\textbf{Step-6:}}}$
Find the 2-digit number using relation given by [3]

Substituting Values

$\implies Two-digit\: No.= 11(7)+1$

$\implies Two-digit\: No.= 78$

$\therefore$
The Required Two-digit No. = $\underline{\large{\textbf{78}}}$

$\underline{\large{\textbf{Verification:}}}$
Verify [1] & [2]

Two digit No. = 78
As per [1], Ten's digit = Unit's digit +1
8 = 7+1
8= 8 ✓

As per [2], No. = 5(sum of it's digits) + 3
78 = 5(7+8)+3
78 = 5(15)+3
78 = 75+3
78 = 78 ✓

Data provided in the Question is Satisfied.

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Answer 2

Answer:

Step-by-step explanation:

According to the problem

Tens digit = x

Units digit=x+1

So number is 10x+x+1

11x+1

By the given statement,

11x+1=5(2x+1)+3

11x+1=10x+5+3

11x+10x=8-1

X=7

So tens digit=7

Units digit=8

Number=78