The digits of a two digits number differ by 3. if the digits are interchanged and the resulting number is added to the original number, we get 99. What can be the original number?.
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Answered by
1
The answer is 45(original no.)
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poonam3863:
63
/36
36 is the answer please explain SIR
kisse aap puchh rhe h
SIR aap explain karo na
Answered by
1
The sum of a two-digit number and the number obtained by interchanging the digits is 11 times the sum of the digits.
Which means,
(10x + y) + (10y + x) = 11(x + y)
The answer is both 10x + y and 10y + x.
Here,
11(x + y) = 99
⇒ x + y = 9 → (1)
Also, given that,
x - y = 3 → (2)
(1) + (2)
⇒ (x + y) + (x - y) = 9 + 3
⇒ 2x = 12
⇒ x = 6
(1) - (2)
⇒ (x + y) - (x - y) = 9 - 3
⇒ 2y = 6
⇒ y = 3
So the original number is,
10x + y = 10 × 6 + 3 = 60 + 3 = 63
and,
10y + x = 10 × 3 + 6 = 36
So the answer is either 63 or 36.
Hope this helps. Plz mark it as the brainliest.
Thank you. :-))
Consider a two digit number. Form another two digit number by interchanging the digits each other. Like considering 47 and forming 74 and vice versa.
If we add the two digit number considered to the two digit number formed, we get a number which is 11 multiplied by the sum of the digits.
Let me write it algebraically. Considering 10x + y. Forming 10y + x. Adding both, we get 11x + 11y, which is 11(x + y).
In this question, the answer is either 10x + y or 10y + x. Both can be. In this question I got 36 and 63. Both can be the answers, not only one. Greatest or least is not a problem here.
Given that the digits of the number differ by 3. We can write it as either x - y = 3 or y - x = 3. According to x - y = 3, we get 63 as answer, and according to y - x = 3, we get 36 as the answer. Because I'm letting the answer as 10x + y.
I took x - y = 3 as second equation in my answer.
Given that the sum of the numbers is 99, which is 11 times the sum of digits, as we discussed earlier. So let it be written as 11(x + y) = 99, then we get x + y = 9 by dividing both sides by 11. This is the first equation.
Add both the equations, we get 2x = 12, thereby getting x = 6.
Subtract second equation from the first equation. We get 2y = 6, thereby getting y = 3.
Now, 10x + y becomes 63 and 10y + x becomes 36. We discussed earlier that both can be the answers. That's all!!!
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