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SURAJ GUPTA

· started a discussion

· 1 Months ago

Solution not clear (Question:99315.0)

please provide alternate solution for this question

Question:
When we multiply a certain two-digit number by the sum of its digits, 405 is achieved. If we multiply the number written in reverse order of the same digits by the sum of the digits, we get 486. Find the number.
Options:
A) 81
B) 45
C) 36
D) 54
Solution:

Ans (b) The sum of two numbers should be factors of 405. A factor search will yield the factor. (look only for 2 digit factors of 405 with sum of digits between 1 to 19).

Also 405 = 5 × 34. Hence: 15 × 27

45 × 9 are the only two options.

i.e. Number × sum of digits = 405.

From these factors pairs only the second pair gives us the desired result.

Hence, the answer is 45.

Alternative method

(10a+b)(a+b)=405 and

(10b+a)(a+b)=486

from these two we can conclude that the last digit of the number should be 5. so, by simplifying the first equation, we get \(10a^2\)+55a+25=405.

thats \(10a^2\)+55a=380.

now a should be an even number..so we check for 2 and then for 4.. which satisfies the equation.giving the answer as 45


Knowledge Expert

· commented

· 1 Months ago

Dear student,
We have updated alternate method. Kindly re-check

Regards
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