How many females achieved a first degree in 1990?

Question

The number of females that achieved a first degree in 1980 was 25,319, in the UK. Over the next ten years this number increased by 33.76%. How many females achieved a first degree in 1990?

Answer 1

This type of question is very often worked by multiplying the starting value (that is, the base value) by the new percent (that is, 100% + percent increase), then rounding.  This is mathematically wrong!

 

The percent given in the problem has already been rounded.  The original number of people and the final number of people are exact integers.

 

You may find the approximate final number by 25319*1.3376, but then you must consider the effect of rounding the percentage:

      25319*1.3376 = 33866.6944 which is close, but not exact, since the percent has been rounded

 

   So,

      33865/25319 = 1.337533078

      33866/25319 = 1.337572574   ** rounds to 1.3376

      33867/25319 = 1.33761207     ** rounds to 1.3376

      33868/25319 = 1.337651566

 

The new number may be 33866 or 33867 (either is correct!).

Answer 2

25,319 (.3376) = 8547.6944

25,319 + 8548 = 33,867 females