1.   x-3/x+3=5/6
2.   3x/5x+2=-4
3.     4x+7/9-3x=1/4
4. The ages of Ravi and Hema are in the ratio 5:7. Four years later,their ages will be in the ratio 3:4.Find their ages.
5. The denominator of a rational number is greater than its numerator by 8.If the numerator is increased by 17 and the denominator is decreased by 1,the number obtained is 2/3.Find the rational number.
6.Three times the smallest of three consecutive odd number decreased by 7 equals twice the largest one. Find the numbers.
7. Robin is 25 years younger than his father. After 5years ,her mother will be three times as old as she will then. Find their present ages.
 

Asked by Krishna | 24th Aug, 2015, 12:36: PM

Expert Answer:

begin mathsize 14px style 1. space space fraction numerator x minus 3 over denominator x plus 3 end fraction equals 5 over 6 6 left parenthesis x minus 3 right parenthesis equals 5 left parenthesis x plus 3 right parenthesis 6 x minus 18 equals 5 x plus 15 6 x minus 5 x equals 15 plus 18 x equals 33  2. space space space fraction numerator 3 x over denominator 5 x plus 2 end fraction equals negative 4 3 x equals negative 4 left parenthesis 5 x plus 2 right parenthesis 3 x equals negative 20 x minus 8 3 x plus 20 x equals negative 8 23 x equals negative 8 x equals negative 8 over 23  3. space space space fraction numerator 4 x plus 7 over denominator 9 minus 3 x end fraction equals 1 fourth 4 left parenthesis 4 x plus 7 right parenthesis equals 1 left parenthesis 9 minus 3 x right parenthesis 16 x plus 28 equals 9 minus 3 x 16 x plus 3 x equals 9 minus 28 19 x equals negative 19 x equals negative 1  end style
begin mathsize 14px style 4. space space space L e t space t h e space p r e s e n t space a g e space o f space R a v i space b e space 5 x space y e a r s space a n d space t h e space p r e s e n t space a g e space o f space H e m a space b e space 7 x space y e a r s. F o u r space y e a r s space h e n c e comma R a v i apostrophe s space a g e space equals space left parenthesis 5 x plus 4 right parenthesis space y e a r s H e m a apostrophe s space a g e equals left parenthesis 7 x plus 4 right parenthesis space y e a r s A c c o r d i n g space t o space g i v e n space c o n d i t i o n comma left parenthesis 5 x plus 4 right parenthesis colon left parenthesis 7 x plus 4 right parenthesis equals 3 colon 4 fraction numerator 5 x plus 4 over denominator 7 x plus 4 end fraction equals 3 over 4 4 left parenthesis 5 x plus 4 right parenthesis equals 3 left parenthesis 7 x plus 4 right parenthesis 20 x plus 16 equals 21 x plus 12 20 x minus 21 x equals 12 minus 16 minus x equals negative 4 x equals 4 T h u s comma space R a v i apostrophe s space a g e equals 5 x equals 5 cross times 4 equals 20 space y e a r s h e m a apostrophe s space a g e equals 7 x equals 7 cross times 4 equals 28 space y e a r s end style

Answered by Rashmi Khot | 25th Aug, 2015, 08:57: AM