Question

If 20 tiles weigh 5 kg. How much does 7 tiles weigh? If a man wants to carry a weight of only 12kg, how many tiles will he be able to carry?

Answer 1

Hint: In the given question, first we find the weight of 1 tile by using the unitary method then multiply it by the number of tiles whose weight is to be found. Later we know that a man carries 12kg of weight only, so here first we find the number of tiles that weights equal to 1 kg then multiply it by the total weight that a man can carry. In this way we will get the required solution.

Complete step-by-step solution:
We have given that,
Weight of the 20 tiles = 5kg
Therefore,
Weight of the 1 tile = \[\dfrac{total\ weight}{total\ number\ of\ the\ tiles}=\dfrac{5}{20}=\dfrac{1}{4}kg\]
Now,
Weight of 7 tiles = \[\dfrac{1}{4}kg\times 7=\dfrac{7}{4}kg=1.75kg\]
Thus, the weight of the 7 tiles is \[1.75kg\].
Now,
1 man carries a weight of 12kg only.
Thus,
Number of tiles that weighs 1kg = \[\dfrac{total\ number\ of\ the\ tiles}{total\ weight}=\dfrac{20}{5}=4tiles\]
Weight of 4 tiles = 1 kg.
Therefore,
Number of tiles that weights total of 12kg = \[4\times 12=48tiles\]

Thus, a man carries a total of 48 tiles that weight equals to 12kg.

Note: While solving these types of questions, students need to remember the unitary method. For unitary methods, we have to find the quantity or the amount needed by 1 student or sometimes it is given in the question and then multiply it by the quantity provided that is to be found. They should be very careful while doing calculations to avoid making errors.