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@swanandk12 I think it is infinity. As x increases the value of F(x) will keep on increasing. So possible values of F(x) are infinite. Hence the sum of possible values F(x) is infinity. Thoughts?

@visheshsahni

No one is perfect here yaar and if you find a mistake in a solution and know the right answer, least thing to do is to share the solution. That's how a forum (should) function right ? :)
Corrected the question.

t + t/12 = 9 (time taken in the return journey is 1/12th the time taken for the onward journey)
t = 108/13 = 8.30 hours
t + t/6 = 9.68 hours?

@shreyasnegi13
There are 10 primes in the given range.
4 also satisfies
9 and 25 won't work because we would already have two 3s and 5s respectively in the numerator
So 10 + 1 = 11 values.

@laavanya-ramaul

120 = I + II + III (Where I - number of students who attended exactly one interview, II - exactly two interviews and III - exactly three interviews)
I > II > III
III is at-least 1

a) maximum number of students who attended exactly 3 companies.
We have to minimize I and II.
Let say x people attended all three. and let x + 1 attended exactly two companies and x + 2 attended exactly one company.
So 3x + 3 = 120
x = 39

@vinaycat2017

120 rupees is the original price
25 rupees down payment means 95 rupees is what we are "Borrowing" from the shop.
Amount paid in instalments = 25 * 4 = 100
So 100 - 95 = 5 is the interest
Now this interest gained (Rs 5) is through the interest gained in the available amount month by month.
5 = 95R/(12 * 100) + 70R/(12 * 100) + 45R/(12 * 100) + 20R/(12 * 100)
5 = 230R/(12 * 100)
R = 6000/230 = 26.09%

@Ishita 120 is correct. Can you share your detailed approach so that others will benefit :)

@Ishita 22.5 is the right answer.

A does 3x and B does x amount of work in a given amount of time.
as work is inversely proportional to the time taken, A takes t days and B takes 3t days to complete a given amount of work.
we know 3t - t = 60 days
t = 30 days
So A takes 30 days and B takes 30 + 60 = 90 days

Together, 1/30 + 1/90 = 4/90 of work will be completed and it will take 90/4 = 22.5 days to finish the work together.

If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)

i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.

Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 80kmph, find the rate at which the train B runs.

Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2 : 3.
Since speed of A is 80 kmph, speed of B must be 80 * (3/2) = 120 kmph

A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 90 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?

Sa/Sb = sqrt(90/40) = 3/2

This gives us that the ratio of the speed of A : speed of B as 3:2. We know that time taken is inversely proportional to speed. If ratio of speed of A and B is 3:2, the time taken to travel the same distance will be in the ratio 2:3. Therefore, since B takes 90 mins to travel from the meeting point to Opladen, A must have taken 60 (= 90*2/3) mins to travel from Opladen to the meeting point

So time taken by A to travel from Opladen to Cologne must be 60 + 40 mins = 1 hr 40 mins

[Credits: Veritasprep]

@vinaycat2017
Let the total distance be d
truck started it journey with 100 kmph and continued so for distance d/3
At d/3 it unloaded 150 cartons, so speed is increased by 20 + 20 + 400/100 = 44% (using successive percentage change formula)
So d/3 distance covered at 100 kmph
next d/3 distance covered at 144 kmph
and last d/3 distance covered at 172 kmph
average speed = 3abc/(ab + bc + ca) = 132 (approx)
d = 132 * 9.82 = 1296 km (approx)