Question

The product of the ages of syam and sunil is 240. if twice the age of sunil is more than syam's age by 4 years, what is sunil's age

Answer 1

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Let age of Sunil =x=x and age of Syam =y=y xy=240  ⋯(1)xy=240  ⋯(1) 2x=y+4⇒y=2x−4⇒y=2(x−2)  ⋯(2)2x=y+4⇒y=2x−4⇒y=2(x−2)  ⋯(2) Substituting equation (2)(2) in equation (1)(1). We get x×2(x−2)=240⇒x(x−2)=2402⇒x(x−2)=120  ⋯(3)x×2(x−2)=240⇒x(x−2)=2402⇒x(x−2)=120  ⋯(3) We got a quadratic equation to solve. Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way. But it is more easy to substitute the values given in the choices in the quadratic equation (equation 33) and see which choice satisfy the equation.  Here, option A is 1010. If we substitute that value in the quadratic equation, x(x−2)=10×8x(x−2)=10×8 which is not equal to 120120 Now try option B which is 1212. If we substitute that value in the quadratic equation, x(x−2)=12×10=120x(x−2)=12×10=120. See, we got that x=12x=12 Hence Sunil's age =12=12 (Or else, we can solve the quadratic equation by factorization as, x(x−2)=120⇒x2−2x−120=0⇒(x−12)(x+10)=0⇒x=12 or −10x(x−2)=120⇒x2−2x−120=0⇒(x−12)(x+10)=0⇒x=12 or −10 Since xx is age and cannot be negative, x=12x=12 Or by using quadratic formula as x=−b±√b2−4ac2a=2±√(−2)2−4×1×(−120)2×1=2±√4+4802=2±√4842=2±222=12 or −10x=−b±b2−4ac2a=2±(−2)2−4×1×(−120)2×1=2±4+4802=2±4842=2±222=12 or −10 Since age is positive, x=12

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