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Question
A person's present age is two - fifth of the age of his mother. After 8 years. he will be one half of the age of his mother . What is the present age of the mother?
30
35
40
50
ANSWER : 3
Descrption
<p>Suppose, mother's age is x, hence person's age is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mn>5</mn></mfrac></math></p><p>After 8 years, mother's age will be x + 8 and person's age will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mn>5</mn></mfrac><mo>+</mo><mn>8</mn><mo>=</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>40</mn></mrow><mn>5</mn></mfrac></math></p><p>According to question,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>8</mn><mo>=</mo><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>40</mn></mrow><mn>5</mn></mfrac><mo>×</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>80</mn></mrow><mn>5</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>40</mn><mo>=</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>80</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>4</mn><mi>x</mi><mo>=</mo><mn>80</mn><mo>-</mo><mn>40</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi>x</mi><mo>=</mo><mn>40</mn></math></p><p>Hence, mother's present age is 40</p><p> </p>
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