A play-school has enough chocolates to supply a class of 50 students for 30…
2025
A play-school has enough chocolates to supply a class of 50 students for 30 days, with every student receiving an equal number of chocolates each day. For the first 10 days, only 20 students were present. How many more students can be accommodated into the group for the remaining days, so that all the chocolates get consumed exactly by the end of the 30 days?
- A.
70
- B.
55
- C.
60
- D.
45
Attempted by 3 students.
Show answer & explanation
Correct answer: D
This is a fixed-total-resource (unitary method) problem: chocolates are supplied at the rate of one chocolate per student per day, so the total stock is fixed as (number of students planned) times (number of days planned). When the number of students present changes partway through, the remaining stock must still be exhausted exactly over the remaining days, so the new daily headcount needed for the rest of the period equals (chocolates remaining) divided by (days remaining).
Total chocolates planned = 50 students x 30 days = 1500 chocolates.
For the first 10 days, only 20 students were present, so chocolates consumed = 20 x 10 = 200 chocolates.
Chocolates remaining after day 10 = 1500 - 200 = 1300 chocolates, to be consumed over the remaining 30 - 10 = 20 days.
Students needed each day for the remaining period = 1300 / 20 = 65 students.
Since 20 students are already present, the number of additional students to accommodate = 65 - 20 = 45.
Cross-check: 20 students x 10 days = 200 chocolates, plus 65 students x 20 days = 1300 chocolates, totalling 200 + 1300 = 1500 -- exactly the original stock, confirming the reallocation is exact.
So, 45 additional students can be accommodated into the group so that all the chocolates are consumed exactly.