Latest TCS Aptitude Question SOLUTION: If 5x+12y=60 then find the minimum value of sqrt(x^2+y^2)?

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If 5x+12y=60 then find the minimum value of sqrt(x^2+y^2)?

Asked In TCS pre (11 years ago)

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Read Solution (7) :

Shashi Shekhar  (11 years ago)

put x=0.we get y=5
so,sqrt(0^2+5^2)=5
and
if y=0 than x=12
thn sqrt(12^2+0^2)=12
so the minimum value is 5 is the ans.

Is this solution Helpfull? Yes (35) | No (9)  

RAKESH  (11 years ago)

5x+12y=60
0r (5/13)x + (12/13)y = 60/13
let x=rcosA, y=rsinA so that r=sqrt(x^2 +y^2)
or r(cosA*cosB+sinA.sinB)=60/13 (if 5/13=cosB then sinB=12/13)
or r*cos(A-B)=60/13
or r=(60/13)/cos(A-B)
FOR r=sqrt(x^2 +y^2) to be minm cos(A-B)maxm=1
so minm value of sqrt(x^2+y^2)=60/13

Is this solution Helpfull? Yes (10) | No (6)  

Rajendra kawade  (11 years ago)

ANSWER is 4.60
Put x=1 then y=4.5 now value of (x^2+y^2) is (1^2+4.5^2)=(1+20.25)=21.25
now Sqrt(21.25)=4.60 which is minimum among all the values.
So ANSWER is 4.60

Is this solution Helpfull? Yes (9) | No (4)  

Dipabali Mahato  (11 years ago)

5*0+12*5=60
ans:5

Is this solution Helpfull? Yes (4) | No (3)  

Sagnik Raha  (11 years ago)

(5x+12y)^2+(12x−5y)^2=(13^2)*(x^2+y^2).
Since 5x+12y is given, we minimize x^2+y^2 by minimizing (12x−5y)^2. The minimum value of this is 0. It follows that the minimum value of 60/13.

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SAPTARSHI MONDAL  (11 years ago)

5x+12y=60
y=5 ans 25

Is this solution Helpfull? Yes (1) | No (4)  

deesheeka ghosh  (11 years ago)

x=0,y=5
ans is5

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