search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
1 vote
76 views
The arithmetic mean of scores of $25$ students in an examination is $50.$ Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being $30,$ then the maximum possible score of the toppers is
in Quantitative Aptitude 2.7k points 5 79 342
retagged by
76 views

1 Answer

1 vote
Let  the sum of scores of students be $x.$

$\Rightarrow \frac{x}{50} = 25$

$\Rightarrow x= 25 \times 50$

$\Rightarrow \boxed{x= 1250}$

For the scores of the top $5$ students to be as high as possible, the score of the bottom $20$ students should be as low as possible.

The minimum score is $30,$ and the scores of the bottom $20$ students are distinct integers.

So, the score of bottom $20$ students must be $30,31,32, \dots, 49.$

Let the score of the topper be $y.$

So, $5y+(30+31+32+ \dots +49) = x$

$\Rightarrow 5y + \frac{20}{2}(30+49) = 1250$

$\Rightarrow 5y+790 = 1250$

$\Rightarrow 5y = 1250-790$

$\Rightarrow 5y = 460$

$\Rightarrow \boxed{y=92}$

$\therefore$ The maximum possible score of the topper is $92.$

Correct Answer $:92$
10.1k points 4 8 30
edited by
Answer:

Related questions

1 vote
1 answer
1
130 views
Anil can paint a house in $12 \; \text{days}$ while Barun can paint it in $16 \; \text{days}.$ Anil, Barun, and Chandu undertake to paint the house for $ ₹ \; 24000$ and the three of them together complete the painting in $6 \; \text{days}.$ If Chandu is paid in proportion to the work done by him, then the amount in $\text{INR}$ received by him is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 130 views
1 vote
1 answer
2
143 views
Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in $45 \; \text{minutes},$ Amal completes exactly $3$ more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after $3 \; \text{minutes}.$ The number of rounds Mira walks in one hour is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 143 views
0 votes
0 answers
3
36 views
The number of distinct pairs of integers $(m,n)$ satisfying $|1 + mn| < |m + n| < 5$ is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 36 views
1 vote
1 answer
4
54 views
A four-digit number is formed by using only the digits $1, 2$ and $3$ such that both $2$ and $3$ appear at least once. The number of all such four-digit numbers is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 54 views
1 vote
1 answer
5
104 views
A park is shaped like a rhombus and has area $96 \; \text{sq m}.$ If $40 \; \text{m}$ of fencing is needed to enclose the park, the cost, in $\text{INR},$ of laying electric wires along its two diagonals, at the rate of $ ₹ \; 125 \; \text{per m},$ is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 104 views
...