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.
A. 51.5 kg
B. 75 kg
C. 37.5 kg
D. 112.5 kg
E. None of these
Answer: Option B
Solution (By Examveda Team)
Step 1: Find the weight of the third box.The third box is 25% heavier than the first box (200 kg).
25% of 200 kg = (25/100) * 200 kg = 50 kg
Weight of the third box = 200 kg + 50 kg = 250 kg
Step 2: Find the weight of the second box.
The second box is 20% heavier than the third box (250 kg).
20% of 250 kg = (20/100) * 250 kg = 50 kg
Weight of the second box = 250 kg + 50 kg = 300 kg
Step 3: Find the weight of the fifth box.
The fourth box (350 kg) is 30% lighter than the fifth box.
This means the fourth box is 70% of the fifth box's weight.
Let the weight of the fifth box be x.
0.7x = 350 kg
x = 350 kg / 0.7 = 500 kg
Step 4: Arrange the weights in ascending order.
The weights are: 200 kg, 250 kg, 300 kg, 350 kg, 500 kg
Step 5: Calculate the average weight of the four heaviest boxes.
Four heaviest boxes: 250 kg, 300 kg, 350 kg, 500 kg
Total weight = 250 + 300 + 350 + 500 = 1400 kg
Average weight = 1400 kg / 4 = 350 kg
Step 6: Calculate the average weight of the four lightest boxes.
Four lightest boxes: 200 kg, 250 kg, 300 kg, 350 kg
Total weight = 200 + 250 + 300 + 350 = 1100 kg
Average weight = 1100 kg / 4 = 275 kg
Step 7: Find the difference in the averages.
Difference = 350 kg - 275 kg = 75 kg
Therefore, the correct option is B: 75 kg
This Question Belongs to Arithmetic Ability >> Average
Read carefully the statement about condition 4
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