i) At a camp , there is sufficient food to last for 400 students for 80 days
After 10 days 50 students left the camp . How much longer will the food last ?
ii). Find the smallest natural number by which 13500 should be
multiplied so that the product so obtained is a perfect cube.
plz solve it properly i have problem in it
Answers
Answer:
Step-by-step explanation:
1) Total Students = 400
Food for them = 80 days
So, Quantity of food = 400 *80 = 32000 man-days
Till 10 days, quantity consumed = 10 *400 = 4000 man-days
Rest Quantity = 32000 - 4000 = 28000 man-days
Remaining students = 400 - 50 = 350
Let remaining food be sufficient for X days.
Now,
350X = 28000
X = 28000/350 = 80 days.
2) Using factorization method
13500 = 5 * 5 * 5 * 2 * 2 * 3 * 3 * 3
If you pair up the factors you can see that we have only 2 number of 2's. Thus for this to be a perfect cube, we should have another 2.
Thus 2 is the smallest number by which 13500 should be multiplied.
Given : At a camp , there is sufficient food to last for 400 students for 80 days .
After 10 days 50 students left the camp .
To Find : How much longer will the food last ?
Solution:
sufficient food to last for 400 students for 80 days .
Total Food Available = 400 * 80 = 32000 Student Days
Food Consumed in 10 Days = 400 * 10 = 4000 Student Days
Food Left = 32000 - 4000 = 28000 Student Days
Students Left = 50
Remaining Students = 400 - 50 = 350
Food Will last further = 28000/350 = 80
Now Food will Last for 10 + 80 = 90 Days
Hence Food will last longer for 90 - 80 = 10 Days
13500 should be multiplied by 2 to get perfect cube
13500 * 2 = 27000 = 30³
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