A farmer’s land is two adjoining trapezoids: T1 with bases 70 m & 50 m, height 20 m; T2 with bases 50 m & 30 m, height 15 m. Land costs ₹60/m². What is the total land cost?

Correct — B. Find each trapezoid's area, add them, then multiply by the rate.

Area of T1 = ½ × (70 + 50) × 20 = ½ × 120 × 20 = 1,200 m²
Area of T2 = ½ × (50 + 30) × 15 = ½ × 80 × 15 = 600 m²
Total area = 1,200 + 600 = 1,800 m²
Cost = 1,800 × 60 = ₹1,08,000 → option (b)

Why the others are wrong

• (a)
  ₹1,58,000 — ₹1,58,000 ÷ 60 = 2,633.3 m², not a whole number, yet both trapezoids have whole-number areas (1,200 m² and 600 m²). No correct working reaches it.
• (c)
  ₹98,000 — ₹98,000 ÷ 60 = 1,633.3 m², again not a whole number, and short of the 1,800 m² the two trapezoids cover.
• (d)
  ₹1,26,000 — ₹1,26,000 pays for 2,100 m² (1,26,000 ÷ 60), 300 m² more than the 1,200 + 600 = 1,800 m² the land measures.

A composite plot is priced piece by piece: find each area separately, add them, then apply the rate once.

Both trapezoids list a 50 m base, but each keeps its own height, 20 m for T1 and 15 m for T2. Neither area borrows anything from the other.

Key facts

• Area of a trapezium = ½ × (sum of parallel sides) × height.
• The area of a composite figure is the sum of the areas of its non-overlapping parts.
• At ₹60/m², every 100 m² costs ₹6,000.

Common traps

• Adding all four bases and using one combined height, instead of working each trapezoid separately.
• Forgetting the ½ in each area, which doubles the total to 3,600 m² and ₹2,16,000, a figure not among the choices.

No directly related past PYQ was found.