There are five boxes in cargo hold. The weight of the first box is 200 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box's weight. The fourth box at 350 kg is 30% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.

To solve this problem, let's calculate the weights of all the boxes.

Let's assume the weight of the first box is x kg.
The weight of the third box is 25% higher than the weight of the first box, so it is 1.25x kg.
The weight of the second box is 20% higher than the weight of the third box, so it is 1.2 * 1.25x = 1.5x kg.
The fourth box is 30% lighter than the fifth box, so if the weight of the fifth box is y kg, then the weight of the fourth box is 0.7y kg.
Given that the fourth box weighs 350 kg, we can set up the equation:
0.7y = 350.
Solving for y, we get:
y = 350 / 0.7 = 500 kg.

So, the weights of the boxes are as follows:
First box: x kg.
Second box: 1.5x kg.
Third box: 1.25x kg.
Fourth box: 350 kg.
Fifth box: 500 kg.

Now, let's find the difference in the average weight of the four heaviest boxes and the four lightest boxes.

The average weight of the four heaviest boxes is (1.5x + 1.25x + 350 + 500) / 4 = (3.75x + 850) / 4.
The average weight of the four lightest boxes is (x + 1.5x + 1.25x + 350) / 4 = (3.75x + 350) / 4.

The difference between the two averages is:
[(3.75x + 850) / 4] - [(3.75x + 350) / 4]
= (3.75x + 850 - 3.75x - 350) / 4
= 500 / 4
= 125×30%= 37.5

Therefore, the correct answer is C

The wt of 4th box 350kg which is 30% lighter than 5th box....Ultimately we can say the wt of 4th box is 70% of the wt of 5th box. 70% of (x)= 350 , than x=500 . So the answer is very correct which is given.

The 5th box is 30% heavier than the 4th box
30% of 350 is 105
350+105=455

Where is 500 from?

4th box is 30% lighter than 5th box and wight of 4th box is 350 kg. Now let wight of 5th is x
so now: X - 30% of X = 350
X - X30/100 =350
X - X 3/10 = 350 TAKE LCM
(10X - 3X) / 10 = 350
7X= 3500
X= 500 so the weight of the 5th is 500.

4th box weight is 350.....but it is 30% less weight of 5th box....
Equation is:
Let,
Weight of 5th box is X
X-30% of X = 350
X=500
So the weight of 5th box is 500

Ohkkk so people are thinking that the answer is 455 no u r wrong
Answer is 500
Because it is said that 5th box is 30 % lighter that means the 350 is 70% of 5th box then how much is 100% it's 500

i think prachi is right ! it should be 455kg

it means 4th box is equal to 70% of fifth box
so that 100% will be weight of fifth box
=100×350/70=500kg

Yes you are right that the value of 5th box is 500 but hoe did you find that ???

4th box is 30% lighter then the 5th... I means 5th box is 30% more than 4th
So weight of 5th box : 350+(30% of 350)
350+[ (30/100) *350]
350+[3*35]
350+105
455kg
So weight of 5th box should be 455kg.

4th box is lighter than 5 th box...So 5th box is 500

5th box will weigh 255kg