Explanation

The area of a rectangle is length × width:

Area = length × width

16 = 8 × width

Divide both sides by 8:

width = 2

The perimeter of a rectangle is 2 × (length + width):

Perimeter = 2 × (8 + 2)

= 2 × 10

= 20

Explanation

 My son’s Uncle is my Brother.

Therefore, My brother’s father is my father.

Explanation

Let the distance between the police officer's house and office be D km.
Let the actual time required to reach the office on time be T hours.

Step 1: Forming Equations

Using the speed-time formula:

$$text{Time} = frac{text{Distance}}{text{Speed}}$$Speed​

Case 1: Walking at 4 km/h

D/4​​=T+5/60​

(since he is 5 minutes late, which is 5/60 hours)

Case 2: Walking at 5 km/h

D5​=T−10/60​

(since he is 10 minutes early, which is 10/60 hours)

Step 2: Solving for Distance

From the first equation:

T=D/4​−5/60​

From the second equation:

T=D/5​+10/60​

Equating both expressions for T:

D/4​−5/60​=D/5​+10/60​

Multiply everything by 60 to clear the fractions:

$$60 times left( frac{D}{4} - frac{5}{60} right) = 60 times left( frac{D}{5} + frac{10}{60} right)$$15D−5=12D+10
$$15D-12D=10+5$$$$3D = 15$$ $$D = 5 text{ km}$$

Explanation

Total = 11 + 5 = 16 

Then 11-5 =6 

6x =1200 

= 1200/ 6 

x = 200

Total amount = 16 x 200 

= 3200

Explanation

- Profit = 10% of selling price = 0.10x

- Cost Price = Rs 2

Now use the relation:  

Cost Price = Selling Price – Profit  

⇒ 2 = x – 0.10x  

⇒ 2 = 0.90x  

⇒ x = 2 / 0.90 = 2.22

Explanation

1. A runs less fast than B → B is faster than A.
2. B runs fast but not faster than C → This means B is either equal to or slower than C.

From this, we can conclude:

• If B is already faster than A and C is at least as fast as B, then C is definitely faster than A.

Final Answer:

C runs faster than A

Explanation

Explanation

Given Information:

• A lifter loads 200 packages per hour.
• A labor loads two quarters (i.e., 2/4 or 1/2) less than 200 packages per hour.
  • 1​/2×200=100
  • So, the labor loads 200 - 100 = 100 packages per hour.
• Together, the lifter and labor load:
  $$200+100=300\text{ packages per hour}$$
• They need to load 1500 packages.
• They take 30 minutes (0.5 hours) rest after every 2 hours of loading.

Step 1: Calculate Total Loading Time Without Breaks

1500/300​=5 hours

So, if they were working continuously, they would need exactly 5 hours.

Step 2: Account for Breaks

• They work for 2 hours, then take a 30-minute (0.5-hour) break.
• In 2 hours, they load:
  $$2\times 300=600\text{ packages}$$
• After 2 hours, they take a 0.5-hour break.
• Continuing this cycle:
  • First 2 hours: 600 packages (then a 30-minute break)
  • Next 2 hours: 600 packages (then a 30-minute break)
  • Remaining: 300 packages, which takes 1 more hour (no need for another break).

Total time including breaks:

$$2+0.5+2+0.5+1=5.5\text{ hours}$$

Step 3: Select the Correct Answer

$$(\mathbf{b})5.5\text{ hours}$$

Explanation

$$0.00049+0.201\times 430$$

Step 1: Multiply0.201 by $430$

$$0.201 times 430 = 86.43$$

Step 2: Add $0.00049$

$$86.43+0.00049=86.43049$$

Step 3: Check the options

None of the given answer choices match 86.43049, so the correct answer is:

$$mathbf{(d) text{none of these}}$$

Explanation

Let's define the five consecutive integers as:

$$n,(n+1),(n+2),(n+3),(n+4)$$

Step 1: Set up the equation

Their product is given as:

$$n(n+1)(n+2)(n+3)(n+4)$$

If we add 30 to this product, the lowest integer should be determined.

Step 2: Checking the answer choices

Let's check $n = 1$:

$$1\times 2\times 3\times 4\times 5=120$$

Adding 30:

$$120 + 30 = 150$$

150 is not a perfect product of five consecutive integers for a lower value of $n$.

Let's check $n = 3$:

$$3 times 4 times 5 times 6 times 7 = 2520$$

Adding 30:

$$2520 + 30 = 2550$$

Again, this does not lead to another valid set of consecutive integers.

Let's check $n = 6$:

$$6 times 7 times 8 times 9 times 10 = 3024$$

Adding 30:

$$3024 + 30 = 3054$$

None of these seem to form a perfect new product. However, since the question asks for the lowest integer in a valid case, and if a valid product exists, we see that $n = 6$ fits the pattern closest.

Final Answer:

$$mathbf{(c) 6}$$