Question

There is a 5digit no. 3 pairs of sum is eleven each. Last digit is 3 times the first one. 3 rd digit is 3 less than the second.4 th digit is 4 more than the second one. Find the digit.



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Answer 1

Answer:

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Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that 5 digit number be abcde

According to statement

➢ Last digit is 3 times the first one.

$\rm :\longmapsto\:e = 3a - - - (1)$

➢ 3rd digit is 3 less than the second digit.

$\rm :\longmapsto\:c = b - 3 - - - - (2)$

➢ 4th digit is 4 more than the second one.

$\rm :\longmapsto\:d = b + 4 - - - - (3)$

➢ Further, given that sum of pair of digits is 11.

Let assume that,

$\rm :\longmapsto\:c + d = 11$

$\rm :\longmapsto\:b + 4+ b - 3 = 11$

[ using equation (2) and (3) ]

$\rm :\longmapsto\:2b + 1 = 11$

$\rm :\longmapsto\:2b = 11 - 1$

$\rm :\longmapsto\:2b = 10$

$\bf\implies \:b = 5$

Put value of b in equation (2) and (3), we get

$\bf\implies \:c = 5 - 3 = 2$

and

$\bf\implies \:d = 5 + 4 = 9$

➢ Now, we get the number as a529e

Now,we get one pair whom sum is 11.

➢ Now, i have to choose other pair whom sum is 11 and also fulfill the requirement that e = 3a

So,

$\rm :\longmapsto\:e + b = 11$

$\rm :\longmapsto\:e + 5 = 11$

$\rm :\longmapsto\:e = 11 - 5$

$\bf\implies \:e = 6$

So,

$\bf\implies \:a = 3$

Hence, we get three pairs whom sum is 11 is

$\rm :\longmapsto\:e + b = c + d = a + d= 11$

Hence,

$\bf\implies \:The \: required \: number \: is \: 25296$