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Unitary Method
Cost of 50 bags of rice is 20000 rupees each weighing 15kg. What would be the cost of 30 bags of rice each weighing 10kg.
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2 Replies
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The cost of 50 bags of rice is given as 20,000 rupees, with each bag weighing 15kg. Now, we need to determine the cost of 30 bags of rice, each weighing 10kg.
To solve this problem, we can use the concept of ratios and proportions. Let’s set up a proportion to find the cost of 30 bags of rice:
Let’s assume x as the cost of 30 bags of rice.
The proportion can be set up as follows:
(50 bags) : (30 bags) = (20,000 rupees) : (x rupees)
Now, let’s solve for x using cross-multiplication. Multiply the numerator of the first ratio (50 bags) by the denominator of the second ratio (x rupees), and multiply the denominator of the first ratio (30 bags) by the numerator of the second ratio (20,000 rupees):
50 * x = 30 * 20,000
Simplifying further:
50x = 600,000
To isolate x, divide both sides of the equation by 50:
x = 600,000 / 50
x = 12,000
Therefore, the cost of 30 bags of rice, each weighing 10kg, would be 12,000 rupees.
In conclusion, based on the given information, we used the concept of ratios and proportions to determine that the cost of 30 bags of rice, each weighing 10kg, is 12,000 rupees. This approach allows us to find the cost of a different quantity of bags while considering the change in weight per bag.
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Unitary method means finding the value of single unit first and then find the required value for n units by multiplying n with the single unit value.
Here acc. to the questions:
Given, cost of 50 bags of rice each weighing 15 kg= 20,000
First we’ll find weight of a unit kg rice:
=> Cost of 1 bag of rice weighing 15kg= 20,000/50= 400
=> Cost of 15 kg rice = 400
=> Cost of 1 kg rice= 400/15= 80/3
Now, we need to calculate cost of 30 bags each weighing 10kg :
Cost of 1 kg rice= 80/3
=> Cost of 10 kg= 80/3 * 10= 800/3
=> Cost of 1 bag of 10kg rice= 800/3
=> Cost of 30 bags of 10kg rice= 800/3 * 30= 8000
Therefore, the cost of 30 bags each weighing 10kg is 8000 rupees.
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