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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
answered-by-expert 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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