Question:
How many girls are there in the class?
Statement (I): There are 90 students in the class.
Statement (II): The ratio of boys to girls is \(7:8\).
How many girls are there in the class?
Statement (I): There are 90 students in the class.
Statement (II): The ratio of boys to girls is \(7:8\).
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To divide a quantity according to a ratio, first find the total number of ratio parts and then calculate the value of one part.
Updated On: Jun 12, 2026
- Statement I alone is sufficient, but Statement II alone is not sufficient.
- Statement II alone is sufficient, but Statement I alone is not sufficient.
- Both statements together are sufficient, but neither statement alone is sufficient.
- Even both statements together are not sufficient.
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The Correct Option is C
Solution and Explanation
Concept:
When a ratio and a total are known, individual quantities can be found.
Step 1: Analyze Statement (I). Total students: \[ 90. \] No information regarding distribution between boys and girls. Statement (I) is insufficient.
Step 2: Analyze Statement (II). Ratio: \[ 7:8. \] Total number is unknown. Possible values: \[ 7,8 \] or \[ 14,16 \] or \[ 21,24. \] Statement (II) is insufficient.
Step 3: Combine both statements. Ratio sum: \[ 7+8=15. \] One part: \[ \frac{90}{15}=6. \] Girls: \[ 8\times 6=48. \] Hence the number of girls is uniquely determined. Therefore both statements together are sufficient.
Step 1: Analyze Statement (I). Total students: \[ 90. \] No information regarding distribution between boys and girls. Statement (I) is insufficient.
Step 2: Analyze Statement (II). Ratio: \[ 7:8. \] Total number is unknown. Possible values: \[ 7,8 \] or \[ 14,16 \] or \[ 21,24. \] Statement (II) is insufficient.
Step 3: Combine both statements. Ratio sum: \[ 7+8=15. \] One part: \[ \frac{90}{15}=6. \] Girls: \[ 8\times 6=48. \] Hence the number of girls is uniquely determined. Therefore both statements together are sufficient.
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