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In a row of girls, Rita and Monika occupy the ninth place from the right end and tenth place from the left end, respectively. If they interchange their places, then Rita and Monika occupy seventeenth place from the right and eighteenth place form the left respectively. How many girls are there in the row?
- a)25
- b)26
- c)27
- d)Data inadequate
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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In a row of girls, Rita and Monika occupy the ninth place from the rig...
Option B
Total no. of girls = 17 + 10 – 1 or 18 + 9 – 1 = 26.
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In a row of girls, Rita and Monika occupy the ninth place from the rig...
7 people between them 
total 9+7+8+1+1
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In a row of girls, Rita and Monika occupy the ninth place from the rig...
Given Information:
- Rita is in the 9th place from the right end of the row.
- Monika is in the 10th place from the left end of the row.
- When they interchange their places, Rita is in the 17th place from the right end and Monika is in the 18th place from the left end.
Analysis:
Let's assume there are 'x' girls in the row.
- From the right end, Rita is in the 9th place, which means there are 8 girls to the right of her.
- From the left end, Monika is in the 10th place, which means there are 9 girls to the left of her.
When they interchange their places:
- From the right end, Rita is in the 17th place, which means there are 16 girls to the right of her.
- From the left end, Monika is in the 18th place, which means there are 17 girls to the left of her.
Solution:
To find the number of girls in the row, we need to find the common number of girls in both cases (before and after interchange).
From the right end:
- Before interchange: 8 girls to the right of Rita
- After interchange: 16 girls to the right of Rita
From the left end:
- Before interchange: 9 girls to the left of Monika
- After interchange: 17 girls to the left of Monika
To find the common number of girls, we can use the concept of the total number of girls in the row minus the position of the girl from one end plus 1.
From the right end:
- Before interchange: Total girls - Rita's position + 1 = x - 9 + 1 = x - 8
- After interchange: Total girls - Rita's position + 1 = x - 17 + 1 = x - 16
From the left end:
- Before interchange: Total girls - Monika's position + 1 = x - 10 + 1 = x - 9
- After interchange: Total girls - Monika's position + 1 = x - 18 + 1 = x - 17
Setting up the equations:
x - 8 = x - 16
x - 9 = x - 17
Simplifying the equations:
-8 = -16
-9 = -17
Since these equations are inconsistent, it means that there is no possible solution to the given information. Therefore, the data provided is inadequate to determine the number of girls in the row.
Hence, the correct answer is option D) Data inadequate.
- Rita is in the 9th place from the right end of the row.
- Monika is in the 10th place from the left end of the row.
- When they interchange their places, Rita is in the 17th place from the right end and Monika is in the 18th place from the left end.
Analysis:
Let's assume there are 'x' girls in the row.
- From the right end, Rita is in the 9th place, which means there are 8 girls to the right of her.
- From the left end, Monika is in the 10th place, which means there are 9 girls to the left of her.
When they interchange their places:
- From the right end, Rita is in the 17th place, which means there are 16 girls to the right of her.
- From the left end, Monika is in the 18th place, which means there are 17 girls to the left of her.
Solution:
To find the number of girls in the row, we need to find the common number of girls in both cases (before and after interchange).
From the right end:
- Before interchange: 8 girls to the right of Rita
- After interchange: 16 girls to the right of Rita
From the left end:
- Before interchange: 9 girls to the left of Monika
- After interchange: 17 girls to the left of Monika
To find the common number of girls, we can use the concept of the total number of girls in the row minus the position of the girl from one end plus 1.
From the right end:
- Before interchange: Total girls - Rita's position + 1 = x - 9 + 1 = x - 8
- After interchange: Total girls - Rita's position + 1 = x - 17 + 1 = x - 16
From the left end:
- Before interchange: Total girls - Monika's position + 1 = x - 10 + 1 = x - 9
- After interchange: Total girls - Monika's position + 1 = x - 18 + 1 = x - 17
Setting up the equations:
x - 8 = x - 16
x - 9 = x - 17
Simplifying the equations:
-8 = -16
-9 = -17
Since these equations are inconsistent, it means that there is no possible solution to the given information. Therefore, the data provided is inadequate to determine the number of girls in the row.
Hence, the correct answer is option D) Data inadequate.
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