Merit-cum-Means Scholarship Shortlist With a Tie-Break
A district education trust has to shortlist three students from six applicants for a merit-cum-means scholarship. Eligibility requires family income at or below ₹2.5 lakh, an aptitude score of at least 70, and attendance of at least 80%. The composite score is 60% aptitude plus 40% interview. Ties are broken first by higher aptitude score, then by lower family income. The data are:
- P: income ₹2.2 lakh, aptitude 78, interview 70, attendance 85%.
- Q: income ₹2.8 lakh, aptitude 82, interview 80, attendance 90%.
- R: income ₹2.4 lakh, aptitude 72, interview 88, attendance 78%.
- S: income ₹2.0 lakh, aptitude 80, interview 76, attendance 82%.
- T: income ₹1.8 lakh, aptitude 75, interview 90, attendance 88%.
- U: income ₹2.5 lakh, aptitude 74, interview 85, attendance 80%.
The trust has one reserved slot for a student from a government school, but none of the six has that certificate. A trustee suggests relaxing the income ceiling to ₹2.8 lakh to include Q.
1. Identify the eligible applicants, compute composite scores, and name the top three.
Read the worked answer
Check eligibility first:
- Q fails income: ₹2.8 lakh > ₹2.5 lakh.
- R fails attendance: 78% < 80%.
- P, S, T and U meet all three criteria.
Composite scores (0.6 × aptitude + 0.4 × interview):
- P: 0.6×78 + 0.4×70 = 46.8 + 28.0 = 74.8
- S: 0.6×80 + 0.4×76 = 48.0 + 30.4 = 78.4
- T: 0.6×75 + 0.4×90 = 45.0 + 36.0 = 81.0
- U: 0.6×74 + 0.4×85 = 44.4 + 34.0 = 78.4
S and U tie at 78.4. The tie-break is higher aptitude: S has 80, U has 74, so S ranks above U. Ranking: T (81.0), S (78.4), U (78.4), P (74.8). The top three are T, S and U.
2. If the income ceiling is raised to ₹2.8 lakh, who enters and who drops out? Show the new ranking.
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Q becomes eligible at ₹2.8 lakh. Q’s composite is:
0.6×82 + 0.4×80 = 49.2 + 32.0 = 81.2
R remains ineligible because attendance is still 78%. The full eligible ranking is now:
- Q: 81.2
- T: 81.0
- S: 78.4
- U: 78.4
- P: 74.8
S still ranks above U on the aptitude tie-break. The top three become Q, T and S. U drops out, and Q enters at the top. This is a policy-sensitive result: a small change in the income ceiling changes both membership and rank order, so the trust should record the rule change before publishing the list rather than adjusting it case by case.
3. The reserved slot cannot be filled because no applicant has the government-school certificate. Should the trust create a waitlist or reduce the shortlist to two? Recommend with reasoning.
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The trust should not silently reduce the merit shortlist to two, because the three general slots and the reserved slot are separate policy instruments. Reducing the general list would confuse a reserved-slot failure with a merit failure and could penalise the third-ranked eligible student.
The better course is to document that the reserved slot could not be filled, keep the three merit selections under the stated criteria, and create a waitlist in rank order for any later vacancy. If trust rules allow an unfilled reserved slot to be converted, that conversion should be approved explicitly by the board and recorded, not inferred by the selection committee. The committee should also state whether the next eligible candidate would be U or P, so that any later decision is transparent.