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 ???
Nabeel (CA) (3288 Points)
28 April 2012Hey 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)
(1051 Points)
Replied 28 April 2012
Nabeel
(CA)
(3288 Points)
Replied 28 April 2012
Nabeel
(CA)
(3288 Points)
Replied 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)
(427 Points)
Replied 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
Tejaswi Kasturi
(student-cpt)
(427 Points)
Replied 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)
(27 Points)
Replied 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)
(21 Points)
Replied 07 May 2015
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