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D Divya Prakash Singh
Let the numerator of the rational number be x. Then denominator will be x + 8. Further, according to question,                       or                      Cross-multiplication gives:                          2(x + 17)  =  3(x + 7) or                   2x + 34  =  3x + 21 or                        x  = 13 Hence the rational number is   .

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D Divya Prakash Singh
Let the present ages of Hari and Harry be 5x and 7x respectively. (Since there are in the ratio of 5:7) Four years from age of Hari will be = 5x + 4 and Harry's age will be = 7x + 4. According to question four years from now, the ratio of their ages will be 3:4. So the equation becomes :                                                   Cross-multiplication gives:                              ...

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D Divya Prakash Singh
We have                        Cross-multiplication gives,                    3(7y + 4)  =  -4(y + 2) or             21y + 12  =  -4y - 8 or              21y + 4y = -8 - 12 or                    25y  =  -20                     

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D Divya Prakash Singh
We have                           Cross-multiplication gives:                       9z = 4z + 60 or           9z - 4z  = 60 or                  5z = 60  or                    z = 12

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D Divya Prakash Singh
We have                By cross-multiplication we get:                 5(3y + 4)   =  -2(2 - 6y) or             15y + 20 = -4 + 12y or              15y - 12y = -4 - 20 or                    3y = -24                         y = -8

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D Divya Prakash Singh
We will convert the given equation into a linear equation by multiplying   (7 - 6x) to both sides. Equation becomes:   9x = 15(7 - 6x) or                               9x = 105 - 90x or                              99x = 105                          

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D Divya Prakash Singh
We observe that the equation is not a linear equation since LHS is not linear. So we multiply 3x to both the sides to make it linear.   We get,         8x - 3 =  2  3x or                   8x - 3 = 6x or                   8x - 6x = 3 or                       2x = 3                        
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