A reduction of 30% in the price of a commodity enables a person to buy 6 items of the commodity more for Rs.700. Find the total quantity being purchased at the reduced price? (PLD 11)
Answers
Answer:
It is based on inverse proportion or product constancy concept. Reduction in price 20% amount of sugar will increase 25%
It means,
25% = 6 Kg. So,
Initially, total Sugar = 6 × 4 = 24Kg. Thus,
Original price of the sugar was,
24024
= Rs. 10 per kg.
Note:
Let initial price of 100 kg Sugar was Rs. 100.
Now, 20% decrease in rate then rate of 100 kg sugar would be Rs. 80.
So,
Rs. 80 = 100 kg sugar.
Rs. 1 = 10080
kg sugar.
Rs. 100 = 100×10080
= 125 Kg sugar.
Increment in sugar = 25 kg.
% increment = 25×100
100
= 25%.
Means 20% rate decrease, 25% of consumption increase.
The total quantity being purchased at the reduced price is 20 items.
Given,
Percentage of reduction in price = 30%
No. of additional quantities bought = 6
Total price of commodity = Rs. 700
To Find,
total quantity being purchased at the reduced price
Solution,
This problem could be solved using the following method.
Let the price of each item of the commodity initially be Rs. x.
Also, let the no. of items of the commodity bought initially by y.
We know that the total price paid is Rs. 700.
Thus, we can deduce the following mathematical relationship:
⇒ xy = 700
Let this be equation (1).
The price of each item of the commodity is Rs. x - 30% of x.
⇒ x - 0.3 x
⇒ 0.7 x
Also, the no. of items of the commodity bought will be y + 6.
The total price paid is Rs. 700 itself.
Thus, we can deduce the following mathematical relationship:
⇒ (0.7x)(y+6) = 700
⇒ 0.7xy + (0.7x)(6) = 700
⇒ 0.7xy + 4.2x = 700
Let this be equation (2).
Substitute equation (1) in equation (2):
⇒ (0.7)(700) + 4.2x = 700
⇒ 490 + 4.2x = 700
⇒ 4.2x = 700 - 490
⇒ 4.2x = 210
⇒ x = 50
Substitute this value of x in equation (1):
⇒ (50)y = 700
⇒ y = 700 ÷ 50
⇒ y = 14
Hence, the price of one item of the commodity initially is Rs. 50 and the no. of items of the commodity bought initially is 14.
The total quantity being purchased at the reduced price is y+6
⇒ 14 + 6
⇒ 20.
Hence, the total quantity being purchased at the reduced price is 20 items.
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