# ICSE Class 8 Answered

**A number of two digits is 3 times more than twice the sum of the digits. And the number formed by reversing the digits is 3 more than 8 times the sum of the digits. Find the number.**

Asked by justjasonpong | 13 Dec, 2018, 03:55: PM

Expert Answer

First statement of the question should be " A number of 2 digits is 3 more than twice the sum of digits " .

Let x is digit in unit place and y is the digit in tens place.

The number is x+10y and sum of digits is x+y. if the digits are reversed, then number with reversed digits is 10x+y

First condition : x+10y = 3+2(x+y) or -x+8y = 3 ................(1)

Second condition : 10x+y = 3+8(x+y) or 2x - 7y = 3 .............(2)

multply both sides of eqn.(1) by 2, we get -2x+16y = 6 ....................(3)

add eqn.(2) and eqn.(3), we get 9y = 9 or y =1

by substituting y=1 in eqn.(1), we get x = 5; Hence the number is 15

Answered by Thiyagarajan K | 13 Dec, 2018, 10:26: PM

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