Question

Mr Ram lived one-sixth of his life in Mumbai, one-twelth of his life in Pune, one-seventh of

his life in Nagpur, half of his life in Hyderabad and remaining nine years in Delhi. iii) .How many years had he lived in Hyderabad ? a) 43 b) 42 c) 18 d) 35​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

 ⇒ option b) 42 is the correct answer  

Step-by-step explanation:

Given data

Mr.Ram lived one - sixth of his life in Mumbai = $\frac{1}{6}$th his life

                   one- twelve th of his life in Pune  = $\frac{1}{12}$th his life  

                   one-seventh of his life in Nagpur = $\frac{1}{7}$th his life    

                            half of his life in Hyderabad = $\frac{1}{2}$ th his life  

                       and remaining 9 years in Delhi = 9 years    

Here we need to find how many years he had lived in Hyderabad      

Let x be the number of year that he had lived

⇒  $\frac{x}{6} + \frac{x}{12}+ \frac{x}{7} + \frac{x}{2} + 9 =$ x

⇒    $\frac{2x+ 1x}{12} + \frac{x}{2} + \frac{x}{7} + 9 =$ x  [ add x/6 and x/12 ]

⇒    $\frac{3x}{12} + \frac{x}{2} + \frac{x}{7} + 9 =$ x      

⇒    $\frac{3x+ 6x}{12} + \frac{x}{7}+ 9 =$ x         [ add 3x/12 and x/2 ]    

⇒    $\frac{9x}{12 } + \frac{x}{7} + 9$   = x            

⇒   $\frac{3x}{4} + \frac{x}{7} + 9 = x$

⇒  $\frac{3x}{4} + \frac{x}{7} -x = - 9$  

⇒   $\frac{21x+ 4x - 28x }{28} = -9$  

⇒ - 3x   =  -9(28)

⇒  x  = 9 (28) /3 = 3(28) = 84

⇒ the number years that he lived = 84 years

Number of years that he had lived in Hyderabad = half of his life

                                                                                      = $\frac{1}{2} (84)$ = 42 years

⇒ option b) 42 is the correct answer