Question

The sum of three consecutive number is 156 . Find the number which is multiple of 13 out of these numbers.​

Answer 1

Let the smallest of three be x

Since the numbers are consecutive, the other two numbers are (x+1) and (x+2)

Their sum = 156

x+x+1+x+2 = 156

3x+3 = 156

3x = 153

x = 51

So the other two numbers are 52 and 53.

52 is the multiple of 13

SO 52 IS THE ANSWER

Answer 2

AnswEr :

$\sf{Let\:us\: Consider\: that\;One \; Number\;be \: x}$

$\sf{So,\:Three\: Consecutive\; Numbers\; are\: x, \: (x + 1),\: \& (x +2)}$

$\large\bold{\underline{\underline{\sf{\pink{According\:to\: Question\:Now,}}}}}$

$\sf{Sum\:of\:Three\: Consecutive\; Numbers\:is\: 156\:\red{[Given]}}$

$\implies\sf\: x + x + 1 + x + 2 = 156 \\ \\ \implies\sf 3x + 3 = 156 \\ \\ \implies\sf 3x = 156 - 3 \\ \\ \implies\sf 3x = 153 \\ \\ \implies\sf x = \cancel\dfrac{153}{3} \\ \\ \implies\sf\large{\underline{\boxed{\sf{\purple{x \:=\:51}}}}}$

$\sf{Our\: Consecutive\: Numbers \: are \:x,\:x + 1, \: x +2 }$

$\sf{Now}$

$\implies\large\boxed{\sf{\purple{51}}}$

$\:\:\:\;\;\sf = (x + 1)$

$\implies\sf 51 + 1$

$\implies\large\boxed{\sf{\purple{52}}}$

$\:\:\:\;\:\sf = (x + 2)$

$\implies\sf 51 + 2$

$\implies\large\boxed{\sf{\purple{53}}}$

Therefore, Our Three Consecutive Numbers are 51, 52 & 53.

Now, We need to Find the Number which is divisible by 13.

So, Numbers are 51, 52 & 53 out of which 52 is divisible by 13.

$\bold{\underline{\sf{Hence,\: 52\:is \: Required\: Answer.}}}$