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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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D Divya Prakash Singh
We have                    0.25(4f – 3) = 0.05(10f – 9) Let us open the brackets:                 f - 0.75 = 0.5f - 0.45 or             f - 0.5f = - 0.45 + 0.75 or                 0.5f  =  0.30    Dividing both sides by 0.5, we get                        f = 0.6

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D Divya Prakash Singh
Let us open the brackets. LHS:      3(5z - 7) - 2(9z - 11)               =  15z - 21 - 18z + 22               =   -3z + 1 RHS:      4(8z - 13) - 17               = 32z - 52 - 17               = 32z - 69 So the equation becomes :   -3z + 1 = 32z - 69 or                           69 + 1 = 32z + 3z  or                               70 = 35z                                 z = 2

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D Divya Prakash Singh
Let us open the brackets Equation becomes:  15y - 60 - 2y + 18 + 5y + 30 = 0 or                               18y - 12 = 0 or                                   18y = 12                               

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D Divya Prakash Singh
Let us open the brackets :    LHS :    3(t - 3) = 3t - 9    RHS :    5(2t + 1) = 10t + 5  The equation is  3t - 9 = 10t + 5 or                        -9 = 10t - 3t + 5 or                        -9 - 5  = 7t or                            -14 = 7t  Therefore              t = -2

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D Divya Prakash Singh
We have                              Multiplying both sides by 6 (as it is LCM of the denomenator.)                            6m - 3(m - 1)  = 6 - 2(m - 2) or                       6m - 3m + 3 = 6 - 2m + 4 or                              3m + 3 = 10 - 2m Transposing -2m to the LHS and 3 to the RHS:                               3m + 2m = 10 - 3  or                              5m = 7          ...

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D Divya Prakash Singh
We have                            Multiplying both sides by 12, we get                           9t - 6 - ( 8t + 12 ) = 8 - 12t or                       9t - 6 - 8t - 12 = 8 - 12t or                           t - 18 = 8 - 12t Transposing -18 to the RHS and -12t to the LHS:                           12t + t = 8 + 18 = 26 or                              13t = 26  Thus,                            t = 2

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D Divya Prakash Singh
We have                      Multiplying both sides by 15 . (because the LCM of denomenator is 15 )             5x - 25 = 3x - 9 Transposing 3x to the LHS and -25 to the RHS.             5x - 3x = -9 + 25 or             2x = 16                    x = 8

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D Divya Prakash Singh
We have                           Multiplying both sides by 6, we get                     6x + 42 - 16x  =  17 - 15x  or                     -10x +42 = 17 - 15x Transposing -15x to the LHS and 42 to the RHS :                        -10x + 15x = 17 - 42 or                          5x = -25 or                             x = -5

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D Divya Prakash Singh
We have                       Multiplying both sides 12. (We multiplied both sides by 12 because it is the lowest common factor.)                     6n - 9n + 10n = 252 or                         7n = 252 or                           n = 36

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D Divya Prakash Singh
The detailed solution of the above-written question is here, We have                                or                             or                            or                        Mutiplying both sides by 6:                           Thus               

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D Divya Prakash Singh
Let the age of Aman's son is x years. So the age of Aman will be 3x years. Ten years ago, the age of Aman's son = x - 10 and Aman's age = 3x - 10. So according to question,                          5(x - 10) = 3x - 10 or                     5x - 50 = 3x - 10 Transposing 3x to the LHS and -50 to the RHS:                         5x - 3x = -10 + 50 = 40 or                           2x  = 40  or   ...

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D Divya Prakash Singh
Let the age of granddaughter is x years. So the age of grandfather is x + 54. Also grandfather is ten times older than his granddaughter. i.e.,                x + 54 = 10x Transposing x to the RHS :                       54 = 10x - x or                   54 = 9x or                       x = 6 Therefore age of granddaughter = 6 years and the age of grandfather = 6 + 54 = 60 years

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D Divya Prakash Singh
Let us assume the number of deer in the herd to be x. Half of a herd of deer are grazing in the field i.e.,   . Now half are remaining. Three fourths of the remaining are playing nearby, implies :                                         Remaining number of deer will be :                                          Given that rest are 9, so                                      Hence number  of deer...

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D Divya Prakash Singh
Let the total shirt material that Hasan bought be x metre. and the total trouser material be y metre. As per the question,                         Thus trouser material      Now we will make another equaion by using cost of the materials. Profit for shirt is 12% i.e., selling price of shirt is                                 and selling price for trouser is                              Hence...

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D Divya Prakash Singh
Let the lenght and breadth of the plot be 11x and 4x repectively. (Since they are in the ratio11:4) We know that the fencing will be done on the boundary of the plot, so we need to calculate its perimeter. Perimeter of rectangle = 2(lenght + breadth) Total cost to fence the plot = Rs.75000 = Rs.100  Perimeter of plot. Thus equation becomes,                           100  2(11x + 4x) = 75000 or ...

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D Divya Prakash Singh
Let us assume that the Shobo's present age be x. So, Shobo's mother's present age = 6x. Shobo's age five years from now will be = x + 5. It is given that Shobo’s age five years from now will be one-third of his mother’s present age. So,                  or             x + 5 = 2x Transposing x to the RHS,                   5 = 2x - x = x Hence Shobo's present age is x = 5 years and      Shobo's...

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D Divya Prakash Singh
Let us assume that the units place of a two digit number is x. Then as per the question, tens place of the number is 3x. Thus the two digit number is 10(3x) + x. If we interchange the digits the number becomes : 10x + 3x      According to the question,                    10(3x) + x + 10x + 3x = 88 or                      30x + 14x = 88 or                            44x  = 88 Dividing both sides...

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D Divya Prakash Singh
Given that sum of the two digits is 9.  Let us assume the digit of units place be x. Then the digit of tens place will be 9-x. Thus the two digit number is 10(9-x) + x Now if we reverse the digits, the number becomes   10x + (9-x). As per the question,                   10x + (9-x) = 10(9-x) + x + 27 or               9x + 9 = 90 - 10x + x + 27 or               9x + 9 = 117 - 9x Transposing -9x...

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D Divya Prakash Singh
Let the No.1 = x Then the second no. No.2 = 5x. Now the question states that if we add 21 to both numbers one number becomes twice of the other. i.e.,   2(x + 21) = 5x + 21  or       2x + 42 = 5x + 21 Transposing 2x to the RHS and 21 to the LHS:             21 = 5x - 2x = 3x or         x = 7 Thus the two numbers are 7 and 35 .    (Since No.2 = 5x) 
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