Gross Profit Calculation for Toy Trucks

Company A produced 500 toy trucks.
- Cost for first 100 trucks = Rs. 50 each
- Cost for next 400 trucks = Rs. 35 each
- Selling price per truck = Rs. 100

Step 1: Calculate total cost
Cost for first 100 trucks:
$$ 100 \times 50 = 5000 \text{ Rs} $$

Cost for remaining 400 trucks:
$$ 400 \times 35 = 14000 \text{ Rs} $$

Total cost = Rs. 5000 + Rs. 14000 = Rs. 19000

Step 2: Calculate total revenue
$$ 500 \times 100 = 50000 \text{ Rs} $$

Step 3: Calculate gross profit
$$ \text{Gross Profit} = \text{Total Revenue} - \text{Total Cost} $$ $$ = 50000 - 19000 = 31000 \text{ Rs} $$

Company A's Gross Profit = Rs. 31,000

Solution:

  M → K  (−2)
  A → C  (+2)
  N → L  (−2)
  G → I  (+2)
  O → M  (−2)
  

  S (−2) → Q  
  W (+2) → Y  
  E (−2) → C  
  E (+2) → G  
  T (−2) → R  
  Y (+2) → A  
  

Statement: “His brother's father is the only son of my grandfather.”

Decode:
• “His brother's father” = the man's (being introduced) father.
• “the only son of my grandfather” = the woman’s father.

Inference: Man’s father = Woman’s father ⟹ They share the same father ⇒ the woman is the man’s sister (paternal sibling).

Correct Relation: Sister

Answer: Option 3

1. Kamal is to the left of Amrita ⇒ K is somewhere left of A.
2. Dipak is to the right of Amrita ⇒ A is left of D.
3. Ankit is between Amrita and Dipak ⇒ order among these three must be A – N – D (from left to right).
4. Now place Kamal (K) to the left of Amrita as required. With four seats, the only arrangement that satisfies all:
   K  –  A  –  N  –  D

Students at the corners: Kamal (left corner) and Dipak (right corner).

Series: 2, 7, 27, 107, 427, ?

Step 1: Look at the pattern.
Each term seems to follow: $$a_{n+1} = 4 \times a_n - 1$$

Step 2: Verify the rule.
• 2 → 4×2 - 1 = 7 ✅
• 7 → 4×7 - 1 = 27 ✅
• 27 → 4×27 - 1 = 107 ✅
• 107 → 4×107 - 1 = 427 ✅

Step 3: Find the next term.
• 427 → 4×427 - 1 = 1707 ✅

Missing Term: 1707

Answer: Option 2

Grid (row-wise):
(72, 24, 6)    (96, 16, 12)    (108, ?, 18)

Pattern: In each row, $$\text{third} = 2 \times \frac{\text{first}}{\text{second}}$$

Check Row 1: \( 2 \times \frac{72}{24} = 2 \times 3 = 6 \) ✅
Check Row 2: \( 2 \times \frac{96}{16} = 2 \times 6 = 12 \) ✅

Apply to Row 3: Let the missing number be \(x\). $$18 = 2 \times \frac{108}{x}  $$

$$\;\Rightarrow\;18= \frac{216}{x}  $$

$$\;\Rightarrow\; x = \frac{216}{18} = 12$$

Missing Number: 12

Answer: Option 1

Given:

• Amit cycled 15 km south.
• Then turned right (west) and cycled 7 km.
• Turned right again (north) and cycled 10 km.
• Finally, turned left (west) and cycled 5 km.

Calculation:

Vertical displacement: \( 15 - 10 = 5 \, \text{km (south)} \)
Horizontal displacement: \( 7 + 5 = 12 \, \text{km (west)} \)
Using Pythagoras theorem:
Distance = √(5² + 12²) = √(25 + 144) = √169 = 13 \, \text{km}

Answer:

Amit needs to cycle 13 km to return home.

Given Series: 7, 14, 28, ...

Pattern: Each term is multiplied by 2.

Formula for the nth term: Tn = 7 × 2n-1

Calculation:

T₁₀ = 7 × 2^10-1 = 7 × 2⁹ = 7 × 512 = 3584

Answer:

The 10th term is 3584.