Income allocation and remaining amount A man spends 2/5 of income on rent, 3/10 on food, and 1/8 on conveyance. If ₹ 2800 remains, find his total spending on food and conveyance together.

Introduction / Context: This question combines fractional budgeting with a known leftover amount to deduce total income. Once income is known, targeted expenses can be computed by applying the relevant fractions.

Given Data / Assumptions:

• Fractions of income: rent = 2/5, food = 3/10, conveyance = 1/8.
• Remaining amount (after all three) = ₹ 2800.
• Total income = I (unknown).

Concept / Approach: Sum the spent fractions, subtract from 1 to get the remaining fraction. Equate that fraction of I to ₹ 2800 and solve for I. Then compute (food + conveyance) as (3/10 + 1/8) * I exactly.

Step-by-Step Solution:Spent fraction = 2/5 + 3/10 + 1/8.Compute common denominator 40: 2/5 = 16/40, 3/10 = 12/40, 1/8 = 5/40.Sum = (16 + 12 + 5)/40 = 33/40.Remaining fraction = 1 − 33/40 = 7/40.Given 7/40 * I = 2800 ⇒ I = 2800 * 40 / 7 = 16000.Food + conveyance = (3/10 + 1/8) * I = (24/80 + 10/80) * 16000 = (34/80) * 16000 = 17/40 * 16000 = 6800.

Verification / Alternative check: Compute each: rent = 2/5 * 16000 = 6400; food = 4800; conveyance = 2000; remaining = 16000 − (6400 + 4800 + 2000) = 2800. All values are consistent.

Why Other Options Are Wrong:₹ 7000, ₹ 5500, ₹ 6700: Each deviates from the exact fraction 17/40 of the derived income.

Common Pitfalls: Arithmetic slips in fraction addition; using 1/10 instead of 3/10; or forgetting to convert to a common denominator. Work with exact fractions to avoid rounding errors.

Final Answer: ₹ 6800