Question
Kumar spent $240 of his allowance on food and 20% of the remaining allowance on transport. He spent 68% of his allowance on food and transport. What percentage of his allowance did he spend on transport?
(1) 48%
(2) 32%
(3) 8%
(4) 4%
(1) 48%
(2) 32%
(3) 8%
(4) 4%
Answers
Answer
How to get (3) 8%?
Answer
To find the percentage of Kumar's allowance spent on transport, we need to follow a step-by-step approach. Let's break down the problem and solve it systematically.
1. Kumar spent $240 of his allowance on food.
2. The remaining allowance after spending on food is not mentioned directly, so we need to calculate it.
- Let's assume Kumar's total allowance is A dollars.
- Kumar spent $240 on food, so the remaining allowance will be A - 240 dollars.
3. Kumar spent 20% of the remaining allowance on transport.
- To find this amount, we need to calculate 20% of (A - 240).
- 20% can be written as 0.2 in decimal form.
- So, the amount spent on transport is 0.2 * (A - 240) dollars.
4. Kumar spent a total of 68% of his allowance on food and transport combined.
- This means that the sum of the amounts spent on food and transport is equal to 68% of his allowance.
- Mathematically, this can be represented as:
$240 + 0.2 * (A - 240) = 0.68 * A
5. Now, we can solve the equation to find the value of A and then determine the percentage spent on transport.
- Expanding the equation:
$240 + 0.2A - 48 = 0.68A
- Combining like terms:
0.2A - 0.68A = 48 - $240
-0.48A = -$192
- Dividing both sides by -0.48:
A = -$192 / (-0.48)
A ≈ $400
6. We have found that Kumar's total allowance is approximately $400.
7. Now, we can calculate the amount spent on transport:
- 20% of (A - 240) = 0.2 * ($400 - $240) = 0.2 * $160 = $32
8. Finally, to find the percentage of Kumar's allowance spent on transport, we divide the amount spent on transport by the total allowance and multiply by 100:
- Percentage spent on transport = ($32 / $400) * 100 ≈ 8%
Therefore, the correct answer is option (3) 8%.
1. Kumar spent $240 of his allowance on food.
2. The remaining allowance after spending on food is not mentioned directly, so we need to calculate it.
- Let's assume Kumar's total allowance is A dollars.
- Kumar spent $240 on food, so the remaining allowance will be A - 240 dollars.
3. Kumar spent 20% of the remaining allowance on transport.
- To find this amount, we need to calculate 20% of (A - 240).
- 20% can be written as 0.2 in decimal form.
- So, the amount spent on transport is 0.2 * (A - 240) dollars.
4. Kumar spent a total of 68% of his allowance on food and transport combined.
- This means that the sum of the amounts spent on food and transport is equal to 68% of his allowance.
- Mathematically, this can be represented as:
$240 + 0.2 * (A - 240) = 0.68 * A
5. Now, we can solve the equation to find the value of A and then determine the percentage spent on transport.
- Expanding the equation:
$240 + 0.2A - 48 = 0.68A
- Combining like terms:
0.2A - 0.68A = 48 - $240
-0.48A = -$192
- Dividing both sides by -0.48:
A = -$192 / (-0.48)
A ≈ $400
6. We have found that Kumar's total allowance is approximately $400.
7. Now, we can calculate the amount spent on transport:
- 20% of (A - 240) = 0.2 * ($400 - $240) = 0.2 * $160 = $32
8. Finally, to find the percentage of Kumar's allowance spent on transport, we divide the amount spent on transport by the total allowance and multiply by 100:
- Percentage spent on transport = ($32 / $400) * 100 ≈ 8%
Therefore, the correct answer is option (3) 8%.
Answered by
GPT 3.5
Let's suppose Kumar's total allowance is x.
He spent 68% of his allowance on food and transport, so he spent 0.68x on food and transport.
He spent 20% of the remaining allowance on transport, so he spent 0.20(0.32x) = 0.064x on transport.
We know that he spent $240 of his allowance on food, so we can set up the equation 0.68x - 240 = 0.064x.
Simplifying this equation, we get 0.616x = 240.
Dividing both sides by 0.616, we find x ≈ 389.610.
To find the percentage of his allowance he spent on transport, we can calculate (0.064x / x) × 100 ≈ 6.4%.
Therefore, the answer is (4) 4%.
He spent 68% of his allowance on food and transport, so he spent 0.68x on food and transport.
He spent 20% of the remaining allowance on transport, so he spent 0.20(0.32x) = 0.064x on transport.
We know that he spent $240 of his allowance on food, so we can set up the equation 0.68x - 240 = 0.064x.
Simplifying this equation, we get 0.616x = 240.
Dividing both sides by 0.616, we find x ≈ 389.610.
To find the percentage of his allowance he spent on transport, we can calculate (0.064x / x) × 100 ≈ 6.4%.
Therefore, the answer is (4) 4%.
Answered by
GPT 3.5
Apologies for the mistake in my previous response. Let's go through the problem again to find the correct answer.
Let Kumar's total allowance be x.
He spent 68% of his allowance on food and transport, so he spent 0.68x on food and transport.
He spent $240 of his allowance on food, so we can set up the equation 0.68x = 240.
Solving for x, we find x ≈ 352.941.
Now, to find the percentage of his allowance he spent on transport, we can calculate (0.32x / x) × 100 ≈ 9.09%.
Therefore, the correct answer is not among the given answer choices.
Let Kumar's total allowance be x.
He spent 68% of his allowance on food and transport, so he spent 0.68x on food and transport.
He spent $240 of his allowance on food, so we can set up the equation 0.68x = 240.
Solving for x, we find x ≈ 352.941.
Now, to find the percentage of his allowance he spent on transport, we can calculate (0.32x / x) × 100 ≈ 9.09%.
Therefore, the correct answer is not among the given answer choices.
Answered by
GPT 3.5
Apologies for the previous incorrect responses. You are correct, the percentage of Kumar's allowance spent on transport is 8%, as calculated step by step above. Thank you for pointing out the error, and I apologize for any confusion caused.
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