Follow BODMAS rule to solve this question, as per the order is given below,

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contains 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contains 'Addition' and 'Subtraction' should be calculated.

Now, the given expression,

4 × ? = 4062 ÷ 5

⇒ 4 × ? = 4062 ÷ 5

⇒ 4 × ? = 812.4

⇒ ? = 812.4/4 

⇒ ? = 203.1

Rules of Approximation:

1. If a number has digits to the right of the decimal less than 5, then just drop the digits to the right of the decimal. The number hence obtained will be the approximated value.

2. If a number has digits to the right of the decimal more than 5, then just drop the digits to the right of the decimal and raise the remaining number by '1'.The number hence obtained will be the approximated value.

Using the same approach we will solve the given expression:

5432.8777 − 3185.992 − 2141.685 + 4876.418 ÷ 203.184

= 5433 − 3186 − 2142 + 4876 ÷ 203

= (5433 + 24) − (3186 + 2142)

= 5457 − 5328

= 129

(56/100) × 450 + ? = 300

⇒ ? = 300 - (56/100) × 450

⇒ ? = 300 - 252

⇒ ? = 48

Solve the given question using following laws of indices:

Laws of Indices:

1. a^m × aⁿ = a^{m+n}

2. a^m ÷ aⁿ = a^{m-n}

3. [(a^m )ⁿ] = a^mn

4.(a)^(1/m) = ^m√a

5. (a)^(-m) =1/a^m

6. (a)^(m/n) = ⁿ√a^m

7. (a)⁰ = 1

Given expression:

The minimum members in the committee will be least common multiple of 12, 16 and 20

LCM of 12, 16 and 20 = 240

So, minimum members in the committee should be 240 to divide them into the exact groups of 12, 16 and 20.

Let the broken pieces out of 12 be x

⇒ The Glass not broken = (12 - x)

Ratio of Unbroken : Broken = x : (12 - x)

⇒ Now For x = 1 ⇒ Ratio = 1 : 11

⇒ Now For x = 2 ⇒ Ratio = 2 : 10 = 1 : 5

⇒ Now For x = 3 ⇒ Ratio = 3 : 9 = 1 : 3

⇒ Now For x = 4 ⇒ Ratio = 4 : 8 = 1 : 2

⇒ Now For x = 5 ⇒ Ratio = 5 : 7

⇒ Now For x = 6 ⇒ Ratio = 6 : 6 = 1 : 1

⇒ Now For x = 7 ⇒ Ratio = 7 : 5

⇒ Now For x = 8 ⇒ Ratio = 8 : 4 = 2 : 1

⇒ Now For x = 9 ⇒ Ratio = 9 : 3 = 3 : 1

⇒ Now For x = 10 ⇒ Ratio = 10 : 2 = 5 : 1

⇒ Now For x = 11 ⇒ Ratio = 11 : 1

Clearly on comparing various ratios we find that ratio which is not possible is 3 : 2

Let the batsman’s average runs for 15 innings be x.

Then, the total runs scored by batsman in 15 innings = 15x

Since, he scored 60 runs in his 16^th inning

Total runs scored by batsman in 16 innings = 15x + 60

Thus, according to question

New average for 16 innings = (x - 4) runs

Therefore, x - 4 = (15x + 60)/16

⇒16(x - 4) = 15x + 60

⇒16x - 64 = 15x + 60

∴ x = 124

∴ New average for 16^th innings = (x - 4) runs = 124 - 4 = 120 runs.

Let the numerator be x and denominator be 6x + 10.

S.I at the rate of 4% for 2 years

SI₁ = (P × 4 × 2)/100 = 8P/100      ----(1)

S.I at the rate of 6% for next 4 years

SI₂ = (P × 6 × 4)/100 = 24P/100      ----(2)

S.I at the rate of 8% for next 3 years

SI₁ = (P × 8 × 3)/100 = 24P/100      ----(3)

∴ Total simple interest

⇒ S.I = SI₁ + SI₂ + SI₃

⇒ S.I = 8P/100 + 24P/100 + 24P/100 = 56P/100

Now according to the question:

⇒ 56P/100 = 1120

⇒ P = 2000

Hence, the required sum is Rs. 2000