How Cheenta works to ensure student success?
Explore the Back-Story

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 ofx 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

Subscribe to Cheenta at Youtube


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 ofx 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

Subscribe to Cheenta at Youtube


Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
Menu
Trial
Whatsapp
Math Olympiad Program
magic-wandrockethighlight