he present AGE of Ram be x yearsLet the present age of Ram's mother be y years.As per the first condition,5 years ago, Ram's mother was five times his age5 years ago,Ram's age = x - 5Mother's age = y - 5Let's represent the first condition mathematically to get our first equation.y - 5 = 5 ( x - 5)y - 5 = 5x - 255x - 25 = y - 55x - y = - 5 + 255x - y = 20 -----> 1As per the second condition,If his mother is now THRICE as old as himRam's age = 3xMother's age = yLet's represent this too mathematically. Here we will get just the value of one of the variables, either x or y.y = 3xSubstitute, y = 3x in equation 1,5x - y = 20 ----> 1Plug in the value of y,5x - 3x = 202x = 20x = x = 10Present age of Ram = x = 10 yearsSubstitute, x = 10 in equation 1,5x - y = 20 ---> 15 ( 10 ) - y = 2050 - y = 20- y = 20 - 50- y = - 30[canceling minus from both sides]y = 30Present age of Mother = y = 30 years•°• Present age of Ram = 10 years.For first CASE :-5 years ago, Ram's mother was five times his agePresent age of Ram = 10 years5 years ago,Ram's age = 10 - 5 = 5 yearsPresent age of Mother = 30 years5 years ago,Mother's age = 30 - 5 = 25 yearsLet's check if the ages satisfies the first condition,Mother's age = 5 ( Ram's age )25 = 5 ( 5 )25 = 25LHS = RHS.For second case :-His mother is now thrice as old as himMother's age = 30 yearsRam's age = 10 yearsLet's check whether the second condition is satisfied or not.Mother = 3 ( Ram's age)30 = 3 ( 10)30 = 30LHS = RHS.Hence the answe is verified.2) 7m-3m+6 = 6m-104m + 6 = 6m - 1016 = 2mm = 81) t +1 /2 - t-3 /3 = 2t + 5/6Cross multiplication of both the dominator with their opposite numerator3t +3 - 2t + 6 = 2t +5t +9 = 2t +59-5 = 2t - tt = 4