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A number consists of two digits. …

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A number consists of two digits. When the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places. Find ? the number

Posted by ☆ Pranal Rewatkar ☆ 7 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Mahanta Bhagat 7 years, 5 months ago

Let the digit at tens place be x and the digit at ones place be y. So, the no.is 10x+y Sum of its digits is x+y So, the divisor is x+y And, quotient is 7 And, remainder is 0 So, by euclid's division lemma, 10x+y=(x+y)×7+0 or, 10x+y=7x+7y or, 3x-6y=0 or, x-2y=0-------------------------------------------------(1) And, according to question, (10x+y)-27=10y+x or, 10x+y-27=10y+x or, 10x-x+y-10y=27 or, 9x-9y=27 or, x-y=3--------------------------------------------------(2) Subtracting (1) from( 2) x-y-x+2y=3-0 or, y=3 Putting y=3 in (2) x=6 So,. x=6 y=3. So, the no. is 63.

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