Maths-
General
Easy

Question

2000 minus 61 k equals 48
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?

  1. The population k years after 1962
  2. The value of k when the population was 48
  3. The difference between the population in 1962 and the population k years after 1962
  4. The average decrease in the population per year from 1962 to k years after 1962

hintHint:

Hint:
We need to understand every term in the equation given.  We are given the number of bird species in a year 1962 and the number of 
birds after k years. So, we are given that the relation between the years passed and the number of birds species satisfy the equation.

The correct answer is: The average decrease in the population per year from 1962 to k years after 1962


    The given equation is
    2000 minus 61 k equals 48
    Given,
    Number of bird species in year 1962 = 2000
    Number of bird species in year 1962+k = 48
    Solving the above equation for k, we get;
    Also, k satisfies the above equation.
    2000 minus 61 k equals 48
    61 k equals 2000 minus 48
    61 k equals 1952
    k equals 32
    Thus, the population of the bird species in the year (1962+32=)1994 is given by 48.
    Rearranging the equation 2000 minus 61 k equals 48, we get
    61 k equals 2000 minus 48
    61 equals fraction numerator 2000 minus 48 over denominator k end fraction
    Clearly, the right hand side of the above equation gives the average decrease in population from 2000 to 48, in k=32 years.
    In other words,
    61 denotes the average decrease in population per year from 1962 to k years after 1962.
    The correct option is D)


    .

    Note:
    This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population years after 1962 is given by 2000-48=1952.

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