Sum of two digit numbers | PRMO-2016 | Problem 7

Try this beautiful problem from Algebra based on Sum of two digit numbers from PRMO 2016.

Sum of two digit numbers | PRMO | Problem 7

Let s(n) and p(n) denote the sum of all digits of n and the products of all the digits of n(when written in decimal form),respectively.Find the sum of all two digits natural numbers n such that $n=s(n)+p(n)$

$560$
$531$
$654$

Key Concepts

Algebra

number system

addition

Check the Answer

Answer: $531$

PRMO-2016, Problem 7

Pre College Mathematics

Try with Hints

Let $n$ is a number of two digits ,ten's place $x$ and unit place is $y$ .so $n=10x +y$ .given that $s(n)$ = sum of all digits $\Rightarrow s(n)=x+y$ and $p(n)$ =product of all digits= $xy$

now the given condition is $n=s(n)+p(n)$

Can you now finish the problem ..........

From $n=s(n)+p(n)$ condition we have,

$n=s(n)+p(n)$ $\Rightarrow 10x+y=x+y+xy \Rightarrow 9x=xy \Rightarrow y=9$ and the value of $x$ be any digit....

Can you finish the problem........

Therefore all two digits numbers are $19,29,39,49,59,69,79,89,99$ and sum= $19+29+39+49+59+69+79+89+99=531$

Other useful links

Try this beautiful problem from Algebra based on Sum of two digit numbers from PRMO 2016.

Sum of two digit numbers | PRMO | Problem 7

Let s(n) and p(n) denote the sum of all digits of n and the products of all the digits of n(when written in decimal form),respectively.Find the sum of all two digits natural numbers n such that $n=s(n)+p(n)$

$560$
$531$
$654$

Key Concepts

Algebra

number system

addition

Check the Answer

Answer: $531$

PRMO-2016, Problem 7

Pre College Mathematics

Try with Hints

Let $n$ is a number of two digits ,ten's place $x$ and unit place is $y$ .so $n=10x +y$ .given that $s(n)$ = sum of all digits $\Rightarrow s(n)=x+y$ and $p(n)$ =product of all digits= $xy$

now the given condition is $n=s(n)+p(n)$

Can you now finish the problem ..........

From $n=s(n)+p(n)$ condition we have,

$n=s(n)+p(n)$ $\Rightarrow 10x+y=x+y+xy \Rightarrow 9x=xy \Rightarrow y=9$ and the value of $x$ be any digit....

Can you finish the problem........

Therefore all two digits numbers are $19,29,39,49,59,69,79,89,99$ and sum= $19+29+39+49+59+69+79+89+99=531$

Other useful links

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