Question

In how many ways a cricketer can score a double century (200




runs) with only boundaries (fours) and over boundaries (sixes)?




a.15



b. 16



c. 17



d. 18

Answer 1

16 or 17 will be the answer i cannot give u a assurance

Answer 2

Taking the no. of fours and sixes to be x and y respectively,

we can say,

4x+6y=200

or x=(100-3y)/2

Now, x must belong to a whole number, thus we can say 3y<100 ,(3y≠100)

Thus max. value of y should be 33.

Now, regarding the equation, (100-3y) should be even, and thus y should also be even.

Thus, max. value of y is 32.

Now, by AP,

32=0+(n-1)2 ⇒n=17(no. of even terms from 32 to 0 is 17)

Thus, in 17 ways, the situation is possible.(Ans.-c)

If considered no.of sixes never to be zero, no.of ways=16 (Ans.-b)