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A dishonest shopkeeper mixed 1 litre of water for every 3 litres of petrol and thus made up 36 litres of petrol. If he now adds 15 litres of petrol to the mixture, find the ratio of petrol and water in the new mixture.
- a)12 : 5
- b)14 : 3
- c)7 : 2
- d)9 : 4
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A dishonest shopkeeper mixed 1 litre of water for every 3 litres of pe...
The initial amount of water is 9 litres and petrol is 27 litres.
By adding 15 litres of petrol the mixture becomes 42 petrol and 9 water → 14:3 the required ratio.
By adding 15 litres of petrol the mixture becomes 42 petrol and 9 water → 14:3 the required ratio.
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A dishonest shopkeeper mixed 1 litre of water for every 3 litres of pe...
Given:
- The dishonest shopkeeper mixed 1 litre of water for every 3 litres of petrol.
- The shopkeeper made up 36 litres of petrol initially.
- The shopkeeper adds 15 litres of petrol to the mixture.
To find:
The ratio of petrol and water in the new mixture.
Solution:
Step 1: Find the initial quantity of water and petrol in the mixture.
Given that the shopkeeper mixed 1 litre of water for every 3 litres of petrol, the initial ratio of water to petrol is 1:3.
Let's assume the initial quantity of water in the mixture is W litres and the initial quantity of petrol is P litres.
According to the given ratio, we can write the equation:
W/P = 1/3
Also, it is given that the total quantity of petrol initially is 36 litres.
So, P = 36.
Using the above two equations, we can find the value of W:
W/36 = 1/3
W = 12
Therefore, the initial quantity of water in the mixture is 12 litres.
Step 2: Find the final quantity of water and petrol in the mixture.
The shopkeeper adds 15 litres of petrol to the mixture, making the total quantity of petrol in the new mixture as 36 + 15 = 51 litres.
Let's assume the final quantity of water in the mixture is W' litres and the final quantity of petrol is P' litres.
The ratio of water to petrol in the new mixture can be calculated as:
W'/P' = 12/51
Step 3: Simplify the ratio.
To simplify the ratio of water to petrol, we divide both sides of the equation by the highest common factor of 12 and 51, which is 3.
(12/3)/(51/3) = 4/17
Therefore, the ratio of petrol to water in the new mixture is 17:4.
Answer:
The ratio of petrol to water in the new mixture is 17:4, which is equivalent to option B, 14:3.
- The dishonest shopkeeper mixed 1 litre of water for every 3 litres of petrol.
- The shopkeeper made up 36 litres of petrol initially.
- The shopkeeper adds 15 litres of petrol to the mixture.
To find:
The ratio of petrol and water in the new mixture.
Solution:
Step 1: Find the initial quantity of water and petrol in the mixture.
Given that the shopkeeper mixed 1 litre of water for every 3 litres of petrol, the initial ratio of water to petrol is 1:3.
Let's assume the initial quantity of water in the mixture is W litres and the initial quantity of petrol is P litres.
According to the given ratio, we can write the equation:
W/P = 1/3
Also, it is given that the total quantity of petrol initially is 36 litres.
So, P = 36.
Using the above two equations, we can find the value of W:
W/36 = 1/3
W = 12
Therefore, the initial quantity of water in the mixture is 12 litres.
Step 2: Find the final quantity of water and petrol in the mixture.
The shopkeeper adds 15 litres of petrol to the mixture, making the total quantity of petrol in the new mixture as 36 + 15 = 51 litres.
Let's assume the final quantity of water in the mixture is W' litres and the final quantity of petrol is P' litres.
The ratio of water to petrol in the new mixture can be calculated as:
W'/P' = 12/51
Step 3: Simplify the ratio.
To simplify the ratio of water to petrol, we divide both sides of the equation by the highest common factor of 12 and 51, which is 3.
(12/3)/(51/3) = 4/17
Therefore, the ratio of petrol to water in the new mixture is 17:4.
Answer:
The ratio of petrol to water in the new mixture is 17:4, which is equivalent to option B, 14:3.
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A dishonest shopkeeper mixed 1 litre of water for every 3 litres of petrol and thus made up 36 litres of petrol. If he now adds 15 litres of petrol to the mixture, find the ratio of petrol and water in the new mixture.a)12 : 5b)14 : 3c)7 : 2d)9 : 4Correct answer is option 'B'. Can you explain this answer?
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