Scholarship Invoice and Monthly Stipend
You are checking a scholarship vendor’s invoice before releasing funds. The question to settle is: what is the monthly stipend per student? Statement (1): The vendor’s annual stipend bill for 24 students is ₹17,28,000. Statement (2): At the same per-student annual rate, adding 6 students would increase the annual bill by ₹4,32,000. The finance officer says either statement alone is enough; the programme manager says neither is enough because “annual” and “monthly” are different units and the number of months is not stated. You know the scheme runs for 12 months, but the invoice does not state it. Your task is to judge sufficiency with and without the 12-month assumption, compute the monthly figure if the assumption is allowed, and state what would change if the scheme ran for 10 months instead.
1. Is Statement (1) sufficient to find the monthly stipend per student? Explain.
Read the worked answer
Statement (1) gives the annual bill for 24 students: ₹17,28,000 / 24 = ₹72,000 per student per year. That is enough for the annual figure. It is not enough for the monthly figure unless the number of months is known. If the scheme is assumed to run for 12 months, monthly stipend = ₹72,000 / 12 = ₹6,000. Without that assumption, the monthly value is indeterminate; the invoice alone does not establish 12 months.
2. Is Statement (2) sufficient on its own?
Read the worked answer
Statement (2) says 6 extra students would add ₹4,32,000 to the annual bill at the same per-student annual rate. Therefore annual stipend per student = ₹4,32,000 / 6 = ₹72,000. This matches Statement (1), but it has the same limitation: it determines the annual rate, not the monthly rate. To convert to monthly, the number of months is still needed. So Statement (2) alone is sufficient for the annual figure but not for the monthly figure unless a month count is assumed or supplied.
3. Resolve the disagreement. What is the monthly figure under the 12-month scheme, and under a 10-month scheme?
Read the worked answer
Both statements independently yield the same annual per-student rate: ₹72,000. With the known 12-month scheme, monthly stipend = ₹72,000 / 12 = ₹6,000. Under a 10-month scheme, monthly stipend = ₹72,000 / 10 = ₹7,200. Strictly, the programme manager is right about the invoice: neither statement alone proves the monthly amount because the month count is missing. The finance officer is right only if the 12-month scheme duration is treated as established background information. The fix is to state the duration on the invoice or add a statement giving the number of months.