CPU ICDSL-DUM-2004 A two digit numb...
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CPU ICDSL-DUM-2004 A two digit number is 5 times the sum of its digits and is also equal to 5 more than twice the product of its digits. Find the number. (CBSE-Delhi-2004C) The cum of two numbers a and bis 15. and the sum of their recindacale 1 .3 Tind

JEE/Engineering Exams
Maths
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given ( : 10 x+y=5(x+y) ) ( 5 x-4 y=0 ) Also ( 10 x+y=5+2 x y ) putting ( mathrm{y}=5 mathrm{x} / 4 ) from equation (1) ( 10 x+5 x / 4=5+2 x(5 x / 4) ) ( (45 x) / 4=5+left(5 x^{2}right) / 2 ) ( 45 x=20+10 x^{2} ) ( 10 x^{2}-45 x+20=0 ) ( 2 x^{2}-9 x+4=0 ) ( (x-4)(2 x-1)=0 ) hence ( x=4 ) or ( 1 / 2 ) but ( x ) is an integer. so ( x=4 ) ( y=5 x / 4=5 ) the number is ( 10 x+y=40+5=45 )
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