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Home » Represent the following situations in the form of quadratic equations: (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age. (ii) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken
Represent the following situations in the form of quadratic equations: (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age. (ii) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken
CBSE | Class 10 | Exercise 4.1 | Quadratic Equations
Represent the following situations in the form of quadratic equations: (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age. (ii) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken

(iii) Let us consider,

Age of Rohan’s = x  years

Therefore, as per the given question,

Rohan’s mother’s age = x + 26

After 3 years,

Age of Rohan’s = x + 3

Age of Rohan’s mother will be = x + 26 + 3 = x + 29

The product of their ages after 3 years will be equal to 360, such that

\left( x~+\text{ }3 \right)\left( x~+\text{ }29 \right)\text{ }=\text{ }360

\Rightarrow ~{{x}^{2}}~+\text{ }29x~+\text{ }3x~+\text{ }87\text{ }=\text{ }360

\Rightarrow ~{{x}^{2}}~+\text{ }32x~+\text{ }87\text{ }\text{ }360\text{ }=\text{ }0

\Rightarrow ~{{x}^{2}}~+\text{ }32x~\text{ }273\text{ }=\text{ }0

Therefore, the age of Rohan and his mother, satisfies the quadratic equation, {{x}^{2}}~+\text{ }32x~\text{ }273\text{ }=\text{ }0 , which is the required representation of the problem mathematically.

(iv) Let us consider,

The speed of train = x  km/h

And

Time taken to travel 480 km = 480/x km/hr

As per second condition, the speed of train = (x – 8) km/h

Also given, the train will take 3 hours to cover the same distance.

Therefore, time taken to travel 480 km =\text{ }480/\left( x+3 \right)\text{ }km/h

As we know,

Speed\text{ }\times \text{ }Time\text{ }=\text{ }Distance

Therefore,

\left( x~\text{ }8 \right)(480/\left( x~+\text{ }3 \right)\text{ }=\text{ }480

\Rightarrow 480~+\text{ }3x~\text{ }3840/x~\text{ }24\text{ }=\text{ }480

\Rightarrow 3x~\text{ }3840/x~=\text{ }24

\Rightarrow 3{{x}^{2~}}\text{ }8x~\text{ }1280\text{ }=\text{ }0

Therefore, the speed of the train, satisfies the quadratic equation, 3{{x}^{2~}}\text{ }8x~\text{ }1280\text{ }=\text{ }0 , which is the required representation of the problem mathematically.

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