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# 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

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=$19+29+39+49+59+69+79+89+99=531$

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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

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=$19+29+39+49+59+69+79+89+99=531$

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