Question

Average monthly expenditure for January--June is ₹ 3200. He spends ₹ 3000 (July), ₹ 3600 (Aug), ₹ 3900 (Sept), ₹ 4200 (Oct). If November’s expenditure is $50%$ of December’s and the average for the entire year is ₹ 3200, find November’s expenditure.

• A. 1600
• B. 1400
• C. 1700
• D. 1500

Hint:

With averages across periods, convert to totals first; then apply given ratios (here, $N=\tfrac{1}{2}D$) to split the remainder.

Answer 1

The Correct Option is D

Step 1: Calculate totals.
Total for 12 months = 12 × ₹ 3200 = ₹ 38400.
Total Jan--Jun = 6 × ₹ 3200 = ₹ 19200.
Total Jul--Oct = ₹(3000 + 3600 + 3900 + 4200) = ₹ 14700.
Spent till Oct = ₹(19200 + 14700) = ₹ 33900.
Step 2: Calculate amount for Nov & Dec.
Remaining = ₹(38400 - 33900) = ₹ 4500.
Let Nov = N and Dec = D, with \(N=\tfrac{1}{2}D \(\Rightarrow\) D=2N.\)
Then \(N+D=3N=₹ 4500 \(\Rightarrow\) N=₹ 1500.\)
\boxed{\text{November’s expenditure }=\ ₹ 1500}