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The ratio of theme park entrance fee for adults and children is 9 ∶ 4 and for particular day ratio of number of adult visitor and number of children is 8 ∶ 13, for that particular day total earning from children visitors is Rs. 26000. Find the difference in amount collected from adult visitors and children visitors.
- a)16200
- b)10000
- c)15400
- d)2000
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The ratio of theme park entrance fee for adults and children is 9 4 a...
Given,
⇒ Ratio of fee for adults and children = 9 ∶ 4
⇒ Ratio of number of adult visitors and children = 8 ∶ 13
Using compound ratio,
⇒ Ratio of earning from adult visitors and children = (9 × 8) ∶ (4 × 13) = 18 ∶ 13
Given,
⇒ Earning from children = 26000
Then,
⇒ Total earning for that day = 26000 × {(18 + 13)/ 13} = 62000
⇒ Earning from adults = 62000 × {18/(18 + 13)} = 36000
⇒ Required difference = 36000 – 26000 = 10000
⇒ Ratio of fee for adults and children = 9 ∶ 4
⇒ Ratio of number of adult visitors and children = 8 ∶ 13
Using compound ratio,
⇒ Ratio of earning from adult visitors and children = (9 × 8) ∶ (4 × 13) = 18 ∶ 13
Given,
⇒ Earning from children = 26000
Then,
⇒ Total earning for that day = 26000 × {(18 + 13)/ 13} = 62000
⇒ Earning from adults = 62000 × {18/(18 + 13)} = 36000
⇒ Required difference = 36000 – 26000 = 10000
Most Upvoted Answer
The ratio of theme park entrance fee for adults and children is 9 4 a...
Given:
- The ratio of theme park entrance fee for adults and children is 9:4.
- The ratio of the number of adult visitors to the number of children visitors for a particular day is 8:13.
- The total earning from children visitors on that particular day is Rs. 26000.
To Find:
The difference in the amount collected from adult visitors and children visitors.
Solution:
Step 1: Finding the Ratio of Adult Visitors and Children Visitors
- Let's assume that the number of adult visitors is 8x and the number of children visitors is 13x.
- Therefore, the ratio of the number of adult visitors to the number of children visitors is 8x:13x.
Step 2: Finding the Entrance Fee for Adults and Children
- The given ratio of the theme park entrance fee for adults and children is 9:4.
- Let's assume the entrance fee for adults is 9y and the entrance fee for children is 4y.
Step 3: Calculating the Amount Collected from Children Visitors
- The total earning from children visitors on that particular day is given as Rs. 26000.
- Therefore, the amount collected from children visitors is 13x * 4y = Rs. 26000.
Step 4: Solving for x and y
- From Step 3, we have 13x * 4y = 26000.
- Simplifying the equation, we get 52xy = 26000.
- Dividing both sides by 52, we get xy = 500.
Step 5: Calculating the Amount Collected from Adult Visitors
- The amount collected from adult visitors is 8x * 9y.
- Substituting the value of xy from Step 4, we have 8x * 9y = 8x * 9 * 500/y.
- Simplifying the equation, we get 8x * 9 * 500/y = 36,000x.
Step 6: Calculating the Difference in Amount Collected
- The difference in the amount collected from adult visitors and children visitors is given by 36,000x - 13x * 4y.
- Substituting the value of xy from Step 4, we have 36,000x - 13x * 4 * 500/x = 36,000x - 26,000x = 10,000x.
Step 7: Finding the Value of x
- To find the value of x, we can equate the amount collected from adult visitors to the total earning from children visitors.
- Therefore, 36,000x = 26,000x.
- Dividing both sides by x, we get 36,000 = 26,000.
- Solving the equation, we find x = 10.
Step 8: Calculating the Difference in Amount Collected (Final Answer)
- Substituting the value of x into the equation from Step 6, we have 10,000x = 10,000 * 10 = Rs. 100,000.
Therefore, the difference in the amount collected from adult visitors and children
- The ratio of theme park entrance fee for adults and children is 9:4.
- The ratio of the number of adult visitors to the number of children visitors for a particular day is 8:13.
- The total earning from children visitors on that particular day is Rs. 26000.
To Find:
The difference in the amount collected from adult visitors and children visitors.
Solution:
Step 1: Finding the Ratio of Adult Visitors and Children Visitors
- Let's assume that the number of adult visitors is 8x and the number of children visitors is 13x.
- Therefore, the ratio of the number of adult visitors to the number of children visitors is 8x:13x.
Step 2: Finding the Entrance Fee for Adults and Children
- The given ratio of the theme park entrance fee for adults and children is 9:4.
- Let's assume the entrance fee for adults is 9y and the entrance fee for children is 4y.
Step 3: Calculating the Amount Collected from Children Visitors
- The total earning from children visitors on that particular day is given as Rs. 26000.
- Therefore, the amount collected from children visitors is 13x * 4y = Rs. 26000.
Step 4: Solving for x and y
- From Step 3, we have 13x * 4y = 26000.
- Simplifying the equation, we get 52xy = 26000.
- Dividing both sides by 52, we get xy = 500.
Step 5: Calculating the Amount Collected from Adult Visitors
- The amount collected from adult visitors is 8x * 9y.
- Substituting the value of xy from Step 4, we have 8x * 9y = 8x * 9 * 500/y.
- Simplifying the equation, we get 8x * 9 * 500/y = 36,000x.
Step 6: Calculating the Difference in Amount Collected
- The difference in the amount collected from adult visitors and children visitors is given by 36,000x - 13x * 4y.
- Substituting the value of xy from Step 4, we have 36,000x - 13x * 4 * 500/x = 36,000x - 26,000x = 10,000x.
Step 7: Finding the Value of x
- To find the value of x, we can equate the amount collected from adult visitors to the total earning from children visitors.
- Therefore, 36,000x = 26,000x.
- Dividing both sides by x, we get 36,000 = 26,000.
- Solving the equation, we find x = 10.
Step 8: Calculating the Difference in Amount Collected (Final Answer)
- Substituting the value of x into the equation from Step 6, we have 10,000x = 10,000 * 10 = Rs. 100,000.
Therefore, the difference in the amount collected from adult visitors and children
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