Monthly income from chained percentages: Pradeep spends 40% on food, then 50% of the remaining on clothes and conveyance, and finally saves one-third of the balance. If his annual savings are ₹19,200, what is his monthly income?

Introduction / Context:This problem chains multiple percentage operations on income: first on the whole, then on the remainder, then a fraction of the final remainder is saved. We reverse the chain using multipliers to recover the base monthly income from annual savings.

Given Data / Assumptions:

• Food = 40% of income.
• Clothes & conveyance = 50% of the remainder.
• From the remaining amount after these expenses, one-third is saved.
• Annual savings = ₹19,200 ⇒ monthly savings = ₹1,600.

Concept / Approach:Let monthly income be S. After food, balance = 0.60S. After clothes & conveyance, balance = 0.50 * 0.60S = 0.30S. Saving = one-third of this balance = (1/3) * 0.30S = 0.10S. Equate 0.10S to ₹1600 to find S.

Step-by-Step Solution:Monthly saving = 0.10SAnnual savings ₹19,200 ⇒ monthly = 19,200 / 12 = ₹1,6000.10S = 1,600 ⇒ S = 1,600 / 0.10 = ₹16,000

Verification / Alternative check:Forward check: Food 40% ⇒ ₹6,400; remainder ₹9,600. Clothes & conveyance 50% of remainder ⇒ ₹4,800; new remainder ₹4,800. Savings = one-third ⇒ ₹1,600 per month, matching data.

Why Other Options Are Wrong:12k, 18k, 20k, 24k do not yield ₹1,600 monthly savings after applying the stated sequence of percentages.

Common Pitfalls:Adding or subtracting percentages as if they were on the original base each time; the second expense is on the remaining amount, not on S.

Final Answer:Rs. 16000