BODMAS Rule:

Given:

To simplify 362 - [26 + {16 + 5(9 ÷ 3)}]

Calculation:

362 - [26 + {16 + 5(9 ÷ 3)}]

or 362 - [26 + {16 + 15}]

or 362 - [26 + 31]

or 362 - 57

or 305

∴ The answer is 305 .

Given:

A, B, and C can do a work in 8, 10, and 12 days, respectively.

Total amount received = Rs. 5550

Concept used:

Efficiency or wages ratio ∝ 1/Time taken

Calculation:

A, B, and C can do a work in 8, 10, and 12 days, respectively.

The ratio = 8 : 10 : 12

The efficiency ratio of A, B, and C = 1/8 : 1/10 : 1/12

= 15 : 12 : 10

So, their wages ratio = 15 : 12 : 10

The share of B = (12/37) × 5550 = Rs. 1800

∴ The share of B (in Rs.) in the amount received is Rs. 1800

Calculation:

Total sales in the year = Rs. 5000 crores

Total sales by Vivo company = 6%

Now,

⇒ (6% of 5000)

⇒ (6/100 × 5000)

⇒ 300 crores

∴ The sales made by Vivo company is 300 crores.

Given:

Longest side of the right-angled triangle: 90 cm One of the other two sides: 54 cm

Solution:

According to the Pythagorean theorem, in a right-angled triangle:

⇒ c² = a² + b²

In this case, we have: c = 90 cm a = 54 cm

Using the Pythagorean theorem, we can find the value of "b":

⇒ 90²  = 54² + b²   

⇒ 8100 = 2916 + b² 

⇒ b² = 8100 - 2916

⇒ b²  = 5184

⇒ b = 72 cm

Now, we can calculate the area of the right-angled triangle using the formula:

Area = (1/2) ×  base × height

Area  = (1/2) ×  54 cm ×  72 cm

Area = 1944 cm²

Therefore, the area of the right-angled triangle is 1944 cm².

The correct answer is option 4) 1944 cm².

Given:

Speed of train = 90 km/h

Time to cross a standing man = 8 seconds.

Length of platform = 250 meters.

Formula used:

Distance = Speed × Time

Calculation:

According to the questions:

Speed of train = 90 km/h

⇒ 90 × (5/18) m/sec.

⇒ 25 m/sec

We know that the distance covered by a train to cross a standing object is the length of the train itself.

So, Distance (Length of the train) = Speed × Time

⇒ Length of train = 25 × 8 m

⇒ Length of train = 200 m.

When the train crosses the platform of length 250 m,

Total distance covered by train = (200 + 250) m

⇒ 450 m

Now, Time to cross the platform = Distance/Speed

⇒ Time to cross the platform = 450/25

⇒ Time to cross the platform = 18 seconds.

∴ The time taken to cross the platform is 18 seconds.

Given:

The volume of a solid cone is 96 π cm3

Height = 8 cm

Formula used:

Volume of a cone = (1/3)πr²h

Total surface area = πr(r + l)

l = √(r² + h²)

Here,

r = radius

h = height

l = slant height

Calculation:

Let the radius be r

According to the question,

(1/3)πr² × 8 = 96π

⇒ (1/3)r² = 12

⇒ r² = 36

⇒ r = 6

Now,

l = √(6² + 8²)

⇒ l = √(36 + 64)

⇒ l = √100

⇒ l = 10

Total surface area = π × 6(6 + 10)

⇒ π × 6 × 16

⇒ 96π

∴ Its total surface area (in cm²) is 96π.

Calculation:

Here, we have (32/243)^k = 8/27

As, we can write 32 as 2⁵ , 243 = 3⁵

Also 8 = 2³ and 27 = 3³

⇒ (2/3)^5k = (2/3)³ 

⇒ 5k = 3

⇒ k = 3/5

Hence, the required value of k is 3/5.

Given:

Ram's average mark in 5 subjects is 80,

Ram's average mark in 6 subjects is 82.

Formula used:

Sum of n numbers = (Average of n numbers) × n

Calculation:

Average marks scored in 5 subjects = 80

Total marks obtained in all 5 subjects = 80 × 5 = 400

Total number of subjects = 6

Average marks scored in 6 subjects = 82

Total marks obtained in all 6 subjects = 82 × 6 = 492

Therefore,

Marks obtained in 6th subject = 492 - 400 = 92

Therefore, '92' is the required answer.

Alternate Method

Ram's average mark in m subjects is x. he must score n marks in his next subject to get average marks of y.

Therefore, 

n = m × (y - x) + y

According to the question,

⇒ n = 5 × (82 - 80) + 82

⇒ n = 5 × 2 + 82

⇒ n = 10 + 82

⇒ n = 92

So, he must score 92 marks in his next subject to get an average mark of 82.

Therefore, '92' is the required answer.

Given:

Deepak's salary = 120% of Raju's salary

Deepak's savings = Rs. 18000 = 48% of his salary

Calculation:

Let, Raju's salary = 100 unit

According to the question,

Deepak's salary = 120% × 100 = 120 unit

Deepak's savings = 48% × 120 = 57.6 unit

Now,

⇒ 57.6 unit = 18000

⇒ 1 unit = 18000/(57.6)

⇒ 1 unit = 18000 × 10/576 = Rs. 312.5

So, Raju's salary = 312.5 × 100 = Rs. 31250

∴ Raju's salary is Rs. 31250.

Given:

Numbers = 5, 6, and 10

Concept used:

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of the numbers.

Calculation:

Factors(5) = 5

Factors(6) = 2 x 3

Factors(10) = 2 x 5

⇒ LCM(5, 6, 10) = 2 x 3 x 5

⇒ 30

Square of 30 = 30 x 30

⇒ 900

∴ The least square number divisible by 5, 6, and 10 is 900.