Question
A team consists of a certain number of members. If 4
people with an average weight of 65 kg leave the team, the average weight of the remaining members decreases by 1.5 kg. If 5 people each weighing 66 kg leave, the average drops by 2.5 kg. What was the total number of people in the team?Solution
ATQ,
Let the number of team members and average weight be 'n' and 'm' kg, respectively.
So, mn - 4 × 65 = (n - 4) × (m - 1.5)
⇒ mn - 260 = mn - 1.5n - 4m + 6
⇒ 4m + 1.5n = 266 --------- (I)
And, mn - 5 × 66 = (n - 5) × (m - 2.5)
⇒ mn - 330 = mn - 2.5n - 5m + 12.5
⇒ 5m + 2.5n = 342.5 -------- (II)
Now solving:
5 × equation I: 20m + 7.5n = 1330
4 × equation II: 20m + 10n = 1370
Subtracting:
7.5n - 10n = -40
⇒ -2.5n = -40
⇒ n = 16
Aman manages to write 256 pages of a book over a span of 24 days, dedicating 8 hours each day to this task. Meanwhile, Pranav, who is known to be 50% mo...
‘P’ alone can paint a house in 18 days, while ‘P’ and ‘Q’ together can do it in 12 days. If ‘Q’ started the work and left after 6 days, ...
‘A’ and ‘B’ can do a piece of work in 25 days and 30 days, respectively. If they started the work together and worked on it for 8 days, then fin...
A person can make 48 flower pots in an hour. Working for 3 hours daily, he has total 660 flower pots that to be made in 4 days time. To accomplish this ...
A group of 8 men or 10 women can complete a certain task in 21 days. How many days will it take for a combination of 10 women and 4 men to complete the...
'Zara' is capable of finishing a specific task in 60 days. On the other hand, 'Armaan' takes 40% more time than 'Zara' to complete the same task, while ...
Ram can do a piece of work in 50 days. He alone worked at it for 20 days and then Lakshman completed alone the rest work in 30 days. In how many days, t...
Mukta takes 8 hours less than Raj to complete the work, and Mukta also takes 32 hours less than Bheem to complete the same work. If Raj and Bheem start ...
A and B together can complete a piece of work in 40 days while B and C together can complete the same work in 36 days. All of three togeth...
Efficiency of A and B are in the ratio of 2 : 3. If both can do a work together in 60 days. Find out how much days A will take to complete the work alone?
Relevant for Exams:
