Question
A fraction becomes 6/7 when 3 is
added to both its numerator and denominator. Similarly, it becomes 7/8 when 5 is added to both its numerator and denominator. Determine the original fraction.Solution
ATQ, Let the original fraction be (x/y). {(x + 3)/(y + 3)} = (6/7) Or, 7x + 21 = 6y + 18 Or, 6y – 7x = 3 -------- (I) Also, {(x + 5)/(y + 5)} = (7/8) Or, 8x + 40 = 7y + 35 Or, 7y – 8x = 5 --------- (II) Equation (I) × 7 - Equation (II) × 6, we get 42y – 49x – 42y + 48x = 21 – 30 Or, x = 9 Putting ‘x’ in equation (I), we get y = (3 + 7 × 9)/6 = 11 so, the fraction = (9/11)
5Â Â Â Â Â Â Â Â Â Â Â Â Â Â 9Â Â Â Â Â Â Â Â Â Â Â Â Â Â 30Â Â Â Â Â Â Â Â Â Â Â 115Â Â Â Â Â Â Â Â Â 582Â Â Â Â Â Â Â Â Â 3483
15Â Â Â Â ...
261Â Â Â Â Â 256Â Â Â Â Â Â 246Â Â Â Â Â Â 231Â Â Â Â Â 211Â Â Â Â Â ?
...20, 30, 40, 55, ?, 160
35Â Â Â 70Â Â Â 105Â Â Â 140Â Â Â 175Â Â Â ?
If 7             16      x    90       171          292
Then, 2x 2 +  1 + x ...
70    191    47    216    ?    245
18Â Â Â Â Â Â Â Â Â Â 434Â Â Â Â Â Â Â Â 642Â Â Â Â Â Â Â Â 746Â Â Â Â Â Â Â Â 798Â Â Â Â Â Â Â Â ?
...41 28 ? 15 67 2
5 ? 205 823 7405 29623
...4 14 44 124 404
...
