# Cpt maths question

Hey Frnds, plz solve this CPT maths question...............

Q. The sum of the digits of the two digit numbers are 10. If 18 is subtracted from it, the digits in the resulting number will be equal. The number is ??? chandu (student)     28 April 2012

Let x = 10's digit of a two digit number
Let y = units digit
Let z = the resulting one

let u assume an equton
"the sum of a two digit number is 10."
x + y = 10----eq1
or
y = (10-x)

18 be subtracted from it,
then eq-2 is:
10x + y - 18 = 10z + z

10x + y = 11z + 18---eq2

Substitute (10-x) for y in eq2
10x + (10-x) = 11z + 18
10x - x = 11z + 18 - 10
9x = 11z + 8
The single digit integer values for x and z are limited to x=7 and z=5 in this equation:
x = 7, y = 3, z = 5
so d 2digit num is:73 Nabeel (CA)     28 April 2012

Frnds, i knew the answer........ I want the process of solving....... Nabeel (CA)     28 April 2012

 Originally posted by : chandu Let x = 10's digit of a two digit number Let y = units digit Let z = the resulting one   let u assume an equton "the sum of a two digit number is 10." x + y = 10----eq1 or y = (10-x)     18 be subtracted from it,  then eq-2 is: 10x + y - 18 = 10z + z   10x + y = 11z + 18---eq2   Substitute (10-x) for y in eq2 10x + (10-x) = 11z + 18 10x - x = 11z + 18 - 10 9x = 11z + 8 The single digit integer values for x and z are limited to x=7 and z=5 in this equation: x = 7, y = 3, z = 5 so d 2digit num is:73 Thnks a lot, but i wont be able to understand the last step....... Plz explain me........... Tejaswi Kasturi (student-cpt)     28 April 2012

the equation is 9x-11z =8 where x,z are integers

The equation is a diophantine equation. It can be solved in the following way.

greatest common divisor of 9 and 11 is 1

11 = 9+2

9 = 4*2 + 1

implies

1 = 9-4*2

1 = 9 - 4(11-9)

1 = 9*5 -(11*4)

now multiply both sides with 8

8 = 9*40-11*32

we can add and subract 99k where k is any integer

8 = 9*(40-11k)-11*(32-9k) (as both the extra terms cancel) for k belonging to integers

so (40,32),(29,23),(18,14),(7,5) ,(-4,-4)......all form the roots of the above equation

in them we need theroots which are greater than 0 and less than 10 hence &(7,5)

usually we don't do all this stuff in exam. we merely try to substitute the answers in multiple choice question in the equation and see whether it is satisfied or not.check out the following link for more information

en.wikipedia.org/wiki/Diophantine_equation Tejaswi Kasturi (student-cpt)     28 April 2012

For solution to general diophantine equation ax+by=c where x,y are integers check out the following linkhttps://en.wikipedia.org/wiki/Extended_Euclidean_algorithm Harsh Modi (1)     01 May 2012

However it is better to solve such questions by Method of Options.

Out of four given options in exam only 1 will be correct.

So take the first option and check whether sum of its digit is 10 or not. If it is 10, then subtract 18 from it and see whether resulting number satisfies given condition.

Repeat the process for other options.

This is the fastest method of solving. sanchi (student)     07 May 2015

The no. Of ways a personcan contribute to a fund out of 1 ten rupee note, 1 five rupee note , 1 two rupee note & 1 one rupee note is view more »