In a class with a certain number of students, if one new student weighing 50 kg is added, then the average weight of the class increased by 1 kg. If one more student weighing 50 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?a)46b)42c)27d)47Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Given information:
- One new student weighing 50 kg is added.
- The average weight of the class increases by 1 kg.
- One more student weighing 50 kg is added.
- The average weight of the class increases by 1.5 kg over the original average.

Let's assume that the original class had 'n' students with an average weight of 'x' kg.

First case:
- After adding one new student of 50 kg, the total weight of the class becomes (nx + 50) kg.
- The new average weight of the class becomes (nx + 50)/(n + 1) kg.
- This new average weight is 1 kg more than the original average weight.
- So, we can write the equation as (nx + 50)/(n + 1) = x + 1.

Second case:
- After adding one more student of 50 kg, the total weight of the class becomes (nx + 100) kg.
- The new average weight of the class becomes (nx + 100)/(n + 2) kg.
- This new average weight is 1.5 kg more than the original average weight.
- So, we can write the equation as (nx + 100)/(n + 2) = x + 1.5.

We have two equations with two variables (n and x). Let's solve them to find the value of x.

Solving the equations:
- Multiplying both sides of the first equation by (n + 1), we get nx + 50 = (n + 1)(x + 1).
- Expanding the right side, we get nx + 50 = nx + x + n + 1.
- Simplifying, we get x = (49 - n)/(n + 1).

- Multiplying both sides of the second equation by (n + 2), we get nx + 100 = (n + 2)(x + 1.5).
- Expanding the right side, we get nx + 100 = nx + 1.5n + 2x + 3.
- Simplifying, we get x = (97 - 1.5n)/(n + 2).

Equating both expressions of x, we get:
(49 - n)/(n + 1) = (97 - 1.5n)/(n + 2).

Solving this equation, we get n = 98/3 = 32.6667 (approx).

Therefore, the original average weight of the class is:
x = (49 - n)/(n + 1) = 47 kg (approx).

Hence, the correct answer is option D.

Similar Defence Doubts

There were 42 students in a hostel. If the number of students is increased by 7 the expenditure on food increases by 49 per day while the average expenditure is reduced by Re 1. What was the initial expenditure on food per day?

The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations is increased by 2, then the median of the new set

A region of area A bounded by a circle C is divided into n regions, each of area A/n, by drawing circles of radii r1, r2, r3, , rn-1such that r < r2< r3< rn-1concentric with the circle C. If pm= rm+1/rm, then which one of the following is correct?

DIRECTIONS:Choose the most appropriate answer.Q. There were 35 students in a hostel. If the number of students be increased by 7, the expenditure on food increases by Rs 42 per day while the average expenditure of students is reduced by Rs1. What was the initial expenditure on food per day?

A man spends 75% of his income and saves the rest. If his income increases by 50% and spending increases by 80%, then what is the percentage change in his savings?

Top Courses for Defence

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams