Explanation

To calculate the total number of people:

$$text{Total number of people} = (text{Your position from the start}) + (text{Your position from the end}) - 1$$

Substitute the values:

$$6+6-1=11$$

Explanation

We are given:

• 4 boxes with weights: 20 kg, 30 kg, 50 kg, and 70 kg.

We need to determine which total weight cannot be made by combining these boxes.

Let's check the combinations:

1. 20 + 30 + 50 + 70 = 170 kg
2. 20 + 30 + 50 = 100 kg
3. 20 + 30 + 70 = 120 kg
4. 20 + 50 + 70 = 140 kg
5. 30 + 50 + 70 = 150 kg

Now check if 160 kg can be made:

• The possible combinations do not result in 160 kg.

Explanation

There are:

• 8 red toys
• 6 green toys
• 7 blue toys

The total number of toys is:

$$8+6+7=21\text{toys}$$

We are asked to find the probability that the toy picked is neither red nor green, which means it must be blue.

The number of blue toys is 7, so the probability is:

17​/21=1/3​

Explanation

We are given:

• 27 bicycles passed the lights test.
• 21 bicycles passed the brakes test.
• 1 bicycle failed both tests.
• There are 30 bicycles in total.

Let:

• $L$ be the set of bicycles that passed the lights test.
• $B$ be the set of bicycles that passed the brakes test.

We need to find how many bicycles passed both tests, which is the intersection of sets $L$a nd $B$, or $L cap B$.

The formula for the union of two sets is:

$$|L\cup B|=|L|+|B|-|L\cap B|$$

We know:

• $|L cup B| = 30 - 1 = 29$ (since 1 bicycle failed both tests).
• $|L|=27$
• $|B| = 21$

Substitute the values into the formula:

$$29 = 27 + 21 - |L cap B|$$ $$29 = 48 - |L cap B|$$ $$|L cap B| = 48 - 29 = 19$$

Explanation

we use the formula:

$$\text{Total Surface Area}=2\pi r(h+r)$$

Where:

• $r$ is the radius of the cylinder.
• $\mathrm{<span\; style="font-family:\; Overpass,\; sans-serif;\; font-size:\; 0.875rem;"><font\; color="\#0000ff">h\; is\; the\; height\; of\; the\; cylinder.</font></span>}$

• Radius $r = 3.5 , text{cm}$
• Height $h = 5.5 , text{cm}$

1. Plug values into the formula:
   $$\text{Total Surface Area}=2\pi \times 3.5\times (5.5+3.5)$$ $$= 2pi times 3.5 times 9$$=2×3.1416×3.5×9
   =2×3.1416×31.5
   =6.2832×31.5
   ≈198.0cm2

Explanation

The temperature in Murree at noon was 16.6°C, and at midnight, it was 20.4°C lower.

To find the temperature at midnight, subtract 20.4°C from the noon temperature:

$$16.6°C - 20.4°C = -3.8°C$$

Explanation

We know that:

1. x + y = 45
2. 4x = 5y - 9

From the first equation, we can express y in terms of x:

y = 45 - x

Substitute this into the second equation:

4x = 5(45 - x) - 9

Expand and simplify:

4x = 225 - 5x - 9

9x = 216

x = 24

Now, substitute x = 24 into the first equation:

24 + y = 45

y = 21

Therefore, the two parts are 24 and 21.

Explanation

• The son's current age be $x$
  
• The man's current age is 5 times the son's age, so the man's age is $5x$.

• Four years ago, the product of their age was 52.

Four years ago:

• The son's age was $x - 4$.
• The man's age was $5x-4$.

According to the problem, the product of their ages 4 years ago is 52:

$$(x-4)(5x-4)=52$$

1. Expand the left side:

   
   

Explanation

Let's define the ages of the three people:

• Let David's age be $D$.
• John's age is 4 years more than David's, so John's age is $D+4$.
• Joe's age is 2 years less than David's, so Joe's age is$D-2$.

The sum of their ages is given as 41:

$$(D)+(D+4)+(D-2)=41$$

1. Simplify the equation:

   $$D + D + 4 + D - 2 = 41$$ $$3D + 2 = 41$$

2. Subtract 2 from both sides:

   $$3D = 39$$

3. Divide both sides by 3:

   $$D = 13$$

So, David is 13 years old.

• John's age is $D + 4 = 13 + 4 = 17$ years.
• In 8 years, John's age will be: $$17 + 8 = 25 text{ years}$$

Explanation

Let's denote the total scholarship grant as "x".

The student spends:

• 15% on food: 0.15x
• 45% on tuition: 0.45x

So, after these expenses, he has:

x - 0.15x - 0.45x = 0.4x remaining.

He then spends 50% of this remaining amount on hostel fees:

0.5 * 0.4x = 0.2x

After this, he is left with Rs 8,000. So, we can set up the equation:

0.4x - 0.2x = 8000

Simplifying the equation:

0.2x = 8000

Dividing both sides by 0.2:

x = 40000

Therefore, the student's scholarship grant is Rs 40,000.