Question

The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?

a)69

b)52

c)85

d)96

answer with full explanation



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Answer 1

$\mathfrak{\huge{\orange{\underline{\underline{Answer :}}}}}$

Let the digits be 'x' and 'y'

So,the number becomes 10(x) + y

= 10x + y

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Given,difference of the digits = 3

x - y = 3

x = 3 + y----------------eqn(1)

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On interchanging the digits,

no.becomes 10y + x

Given that If the digits are interchanged, and the resulting number is added to the original number, we get 143

So,

10x + y + 10y + x = 143

11x + 11y = 143

11(x + y) = 143

x + y = $\sf\frac{143}{11}$

x + y = 13--------------------eqn(2)

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From equation 1,we found that x = 3 + y

Substitute x = 3 + y in equation 2

3 + y + y = 13

3 + 2y = 13

2y = 13 - 3

2y = 10

y = $\sf\frac{10}{2}$

y = 5

We found that x = 3 + y

Substitute y = 5

x = 3 + 5

x = 8

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We assumed no. = 10x + y

Number = 10(8) + 5

Number = 80 + 5

Number = 85

Therefore,Number = '85'

Therefore,the correct option is 'C'

Answer 2

Hi mate

• Let the two digit no.be xy.

• The digit of a two digit no. differ by 3 .
• Hence,x-y=3(i).......

• The digit are interchanged and the resulting number is added to the original number we get 143.

10x+y+10y+x=143

11x + 11y=143

x+y=13......(ii)

Solving (i) and (ii)we get x=8 and y=5

• Hence ,The original no.is 85.

Hope It helps dear