KCC's Quizzes AQQ231 about Birthdays and Cake Candles

1. Let's call Mary's age as n. Sum of n consecutive integers = n(n+1)/2 = 946. That gives us n=43. Mary is 43 years old today.

2. Let's call Helen's age as n and Ann's age as n+5. n(n+1)/2 + (n+5)(n+6)/2 = 1687. Solving that gives us, Helen's age as 38, and Ann's age as 43.

1. n(n+1)/2=946 --> n=43 (sum of first consecutive integers)

2. If m is the age of Ann, the age of Helen is m-5. So m(m+1)/2 + (m-5)(m-4)/2 = 1687. By solving the equation you get m= 43, so Anne is 43 and Helen is 38.

You can also calculate this easily in Excel. Just make a column (column A) with numbers 1,2,3, etc. In the column next to it calculate the number of candles. The first cell (B1) gets: SUM($A$1:A1) and drag this down. You will see that at age 43 946 candles have been blown out. Now copy both columns with an offset of 5 downwards and you will get the results for a second person 5 years younger. Now make a new column with the sum of the candles of each sister and you will get the total number of candles blown out by both sisters. You will easily find that for 1687 sister 1 is 43 and sister 2 is 38.

1 + 2 + 3 ... + n = n(n+1)/2  is the series.

1.   Mary has blown 946 candles.
       n(n+1)/2 = 946
     solving for n we get  n=86/2 = 43
      Mary now is 43 years  old.

2.  If Ann is A years and Helen is A-5 years of age.
       A(A+1)/2  +  [A-5](([A-5]+1)/2 = 1687

     solving for A , we get.  A= 43 so H =43-5=38

Ann is 43 years of age  and Helen is 38 years of age.

Mary and Ann age will be 43 and Helen will be of 48.
As no of candles has blow is 1+2+3+4.......n that is n(n+1) /2 and after calculation it will be 43.
For Ann and Helen if their age is n and n+5 then no of candles blow will be (1+2+3+4..... n) +(1+2+3+4..... n+5) so after calculation value of n will be 38 so n+5= 43

1. Mary is 43 years old.
2. Ann is 43 years old and Helen is 38 years old.
The result can be easily found using Excel:

Thanks Rahul for your prompt reply! Answers will be confirmed next week! Stay tuned!

Merci beaucoup Gaetano! Answers will be confirmed soon!

Yeah Fons,

Any tools, methods including crystal ball are accepted! what counts is the final result! Here also, your answers will be conformed next week!

Thanks a lot Rajesh for your prompt reply! Stay tuned for the official answers next week!