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A two digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number the digits are reversed find the number

Posted by Aishwarya Nagpal 6 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 6 years, 8 months ago

Let x = ones digit
and y = tens digit
then from "a two digit number is 4 more than 6 times the sum of its digits":
x + 10y = 6(x+y)+4
x + 10y = 6x+6y+4
10y = 5x+6y+4
4y = 5x+4. ......... (i)
and, from "if 18 is subtracted from the number,the digits are reversed.find the number"
x+10y -18 = y+10x
10y -18 = y+9x
9y -18 = 9x
y -2 = x
substitute the above into (i)
4y = 5x+4
4y = 5(y-2)+4
4y = 5y-10+4
4y = 5y-6
4y+6 = 5y
6 = y
substitute above into (i), we get
4y = 5x+4
4(6) = 5x+4
24 = 5x+4
20 = 5x
4 = x
The number is 64.

2Thank You

Arman Dodhiya 5 years, 9 months ago

-8

4Thank You

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