Question

$\huge{\underline{\underline{\mathfrak{Question\::}}}}$ 'abc' is a number. Where a, b, c each of them is a single digit. If (a - c) = 5 then, what's the value of (abc - cba) ? Answer with quality! Don't spam.Moderators or Brainly Stars,answer it plz.​

Answer 1

Question :--- abc' is a number. Where a, b, c each of them is a single digit. If (a - c) = 5 then, what's the value of (abc - cba) ?

Solution :---

→ Let us assume that , the three digit number be :-- 100a + 10b + c ..

when we interchange the Positions of This number we get :-- 100c + 10b + a

Now, if we subtract them , we get, :----

→ (100a + 10b + c) - (100c + 10b + a)

→ 100 a - a + 10b - 10b + c - 100c

→ 99a - 99c

→ 99(a-c) ------------- Equation (1)

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Now, in Question value of (a-c) is given = 5

From Equation (1) we can say that, any three digit Number when Interchange , and we subtract it From the Original number , this Must be Divisible by 99...

✪✪✪ Remember This.. ✪✪✪

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Now, lets See Multiple of 99 , that are three digit numbers

are :---- 198 , 297, 396, 495 , 594, 693

These are the Multiple of 99 .

Now, in Question it is given that, (a-c) = 5 .

Here a and c are at unit place and at Hundredth place .

So, Lets check now,

→ 198 = 8-1 = 7 ❎

→ 297 = 7-2 = 5 ✅

→ 396 = 6-3 = 3 ❎

→ 495 = 5-4 = 1❎

→ 594 = 5-4 = 1❎

→ 693 = 6-3 = 3❎

→ 792 = 7-2 = 5✅

→ 891 = 8-1 = 7 ❎

From this we can see that, our Real number that satisfy the condition is 792 .

Now, we have to Find :-- (abc - cba)

Either we can Find by subtracting (792 - 297) or, now we can put value of (a-c) in Equation (1) now, and we simply get our answer ...

⛬ (abc - cba) = 99 * 5 = 495 .(Ans) ..

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Answer 2

$\huge \mathbb{ \underline{ \underline\red{ \red{S{ \pink{O{ \blue{L{ \purple{U{ \orange{T { \red{I{ \blue {O{ \green {N{ \: :-}}}}}}}}}}}}}}}}}}}$

$\: \: \:$

$\sf \pink{ \underline{We \: Have, }}$

$\tt{ABC \: where \: A, B \: and \: C \: are \: digits.}$

$\sf \pink{ \underline{Then}}$

$\tt{ABC = 100 A + 10B + C}$

$\sf \pink{ \underline{Also, }}$

$\sf{CBA = 100C + 10B + A}$

$\sf \pink{ \underline{We \: need , }}$

$\tt{ABC - CBA}$

$\tt= (100A + 10B + C)- (100 - C + 10B + A)$

$\tt{= 100A + 10B + C - 100C - 10B - A}$

$\tt{= 100A - A + 10B + 10B + C - 100C}$

$\tt{= 99A - 99C}$

$\sf \red{(taking \: Common \: factor \: 99)}$

$\tt= 99 (A - C)$

$\sf \pink{ \underline{Now,}}$

$\tt{ABC - CBA = 99 (5)}$

$\tt{ABC - CBA = 495}$

$\sf \pink{ \underline{Hence, }}$

$\: \:$

$\large\boxed{ \sf{ \red{ABC - CBA = 495}}}$

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