Number System
If the numerator of a fraction is decreased by 12.5% and the denominator is increased by 180% the resultant fraction is 1/2. What is the original fraction ?
Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5.Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197.
Let the numbers be x, x + 2, x + 4, x + 6, and x + 8Avg = x + x + 2 + x + 4 + x + 6 + x + 8/5 = 40Therefore, 5x + 20 = 200Therefore, x = 180/5 = 36Therefore, r = x + 4 = 40 s = x + 6 = 42Therefore, Product = 1680
Let the present age of the father be 'x' and that of the son be 'y'. Then x/y = 8/3∴ 3x = 8y Further, x + 12/y + 12 = 2/1 ∴ x + 12 = 2y + 24 ∴ x - 2y = 12 ......(ii)From eqn (i) and (ii), x = 48, y = 18 ∴ sum = 66 yrs.
EXAMIANS