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The price of sugar is decreased by 20%, due to which a family purchases 20 kg more sugar for Rs. 400. Find the original price per kg of the sugar.
- a)Rs. 4/kg
- b)Rs. 6/kg
- c)Rs. 10/kg
- d)Rs. 5/kg
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The price of sugar is decreased by 20%, due to which a family purchase...
Let the original price of the sugar be 100x,
⇒ After 20% decrease, price would be 80x
⇒ Ratio = 100x ∶ 80x = 5x ∶ 4x
Due to this a family purchases 20 kg more sugar for Rs. 400,
⇒ x = 20
⇒ original consumption of sugar = 20 × 4 = 80 kg
∴ original price of sugar = 400/80 = Rs. 5/kg
⇒ After 20% decrease, price would be 80x
⇒ Ratio = 100x ∶ 80x = 5x ∶ 4x
Due to this a family purchases 20 kg more sugar for Rs. 400,
⇒ x = 20
⇒ original consumption of sugar = 20 × 4 = 80 kg
∴ original price of sugar = 400/80 = Rs. 5/kg
Alternative solution:
Let the original price of 1 kg sugar be x and quantity purchased for Rs. 400 be y kg
So, xy = 400
So, xy = 400
When price is reduced by 20%, price of 1 kg sugar = 0.8x and the quantity of sugar purchased for Rs. 400 will be y + 20 kg
So, (0.8x) × (y + 20) = 400
0.8xy + 16x = 400
320 + 16x = 400
16x = 80
∴ x = Rs. 5/Kg
So, (0.8x) × (y + 20) = 400
0.8xy + 16x = 400
320 + 16x = 400
16x = 80
∴ x = Rs. 5/Kg
Most Upvoted Answer
The price of sugar is decreased by 20%, due to which a family purchase...
Given:
- The price of sugar is decreased by 20%
- A family purchases 20 kg more sugar for Rs. 400
To find:
- The original price per kg of the sugar
Solution:
Let's assume that the original price per kg of sugar was Rs. x.
After the decrease of 20%, the new price per kg of sugar will be (100-20)% of x, which is 80% of x or 0.8x.
We know that the family purchased 20 kg more sugar for Rs. 400. So, we can form the equation:
20(0.8x) - 20x = 400
Simplifying the equation, we get:
16x = 400
x = 25
Therefore, the original price per kg of sugar was Rs. 25.
But the options provided are not in rupees 25, so we need to convert it into the provided options.
The original price per kg of sugar in rupees 5 would be Rs. 25/5 = Rs. 5.
Hence, the correct answer is option D, Rs. 5/kg.
- The price of sugar is decreased by 20%
- A family purchases 20 kg more sugar for Rs. 400
To find:
- The original price per kg of the sugar
Solution:
Let's assume that the original price per kg of sugar was Rs. x.
After the decrease of 20%, the new price per kg of sugar will be (100-20)% of x, which is 80% of x or 0.8x.
We know that the family purchased 20 kg more sugar for Rs. 400. So, we can form the equation:
20(0.8x) - 20x = 400
Simplifying the equation, we get:
16x = 400
x = 25
Therefore, the original price per kg of sugar was Rs. 25.
But the options provided are not in rupees 25, so we need to convert it into the provided options.
The original price per kg of sugar in rupees 5 would be Rs. 25/5 = Rs. 5.
Hence, the correct answer is option D, Rs. 5/kg.
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Community Answer
The price of sugar is decreased by 20%, due to which a family purchase...
EXPENSES= PRICE×CONSUMPTION (P=PRICE, C= CONSUMPTION) (PRICE REDUCE BY 20% SO SUPPOSE PRICE IS EQUAL TO 1 THEN 20% WILL BE 0.8P)
400= P×C (EQ.I)
400= 0.8P×(C+20)
(C+20= CONSUMPTION INCREASE BY 20 KG MORE)
FROM EQ.I
P×C= 0.8P×(C+20)
C=0.8C+(0.8×20)
C-0.8C=4
0.2C=4
C=4/0.2= 20
PUT C VALUE IN EQ.1
400=P×20
P=400/20=5Kg
so the original price of sugar is 5kg
400= P×C (EQ.I)
400= 0.8P×(C+20)
(C+20= CONSUMPTION INCREASE BY 20 KG MORE)
FROM EQ.I
P×C= 0.8P×(C+20)
C=0.8C+(0.8×20)
C-0.8C=4
0.2C=4
C=4/0.2= 20
PUT C VALUE IN EQ.1
400=P×20
P=400/20=5Kg
so the original price of sugar is 5kg
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The price of sugar is decreased by 20%, due to which a family purchases 20 kg more sugar for Rs. 400. Find the original price per kg of the sugar.a)Rs. 4/kgb)Rs. 6/kgc)Rs. 10/kgd)Rs. 5/kgCorrect answer is option 'D'. Can you explain this answer?
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