Follow BODMAS rule to solve this question, as per the order 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 contain 'Division' and 'Multiplication' are calculated,

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

Now, the given expression,

28 × 104 ÷ (28 – 21 + 6) + 3 = ?

⇒ ? = 28 × 104 ÷ 13 + 3

⇒ ? = 28 × 8 + 3

⇒ ? = 227 

Given Equation is,

3.2% of 500 × 2.4% of ? = 230.4

⇒ 0.032 × 500 × 0.024 × ? = 230.4

⇒ 0.384 × ? = 230.4

⇒ ? = 600

The given expression:

Given,

⇒ Average = Sum of terms/Number of terms

For Arithmetic Progression,

If Sum of terms = S_n and first term of progression = a, common difference = d and n = number of terms-

Average of first 20 terms of Arithmetic Progression = 675/20 = 33.75

∴ Average of first 20 terms of Arithmetic Progression = 33.75

Ten kg of solution prepared by Adya will initially contain :

Amount of water = 10 − 4.53125 = 5.46875 kg

She has been instructed to prepare the solution by using sugar and water in the ratio 35 ∶ 29 but she prepared in the ratio 29 ∶ 35 which clearly means, she used less quantity of sugar.

Keeping the quantity of water same, let she adds x kg of sugar to it.

⇒ 131.40625 + 29x = 191.40625

⇒ 29x = 60

∴ x = 2.07 kg

∴ Adya will have to add 2.07 kg of sugar more to prepare the syrup as per instructions.

⇒ 131.40625 + 29x = 191.40625

⇒ 29x = 60

∴ x = 2.07 kg

∴ Adya will have to add 2.07 kg of sugar more to prepare the syrup as per instructions.

Given, (X + Y)/2 = 23

⇒ X + Y = 46                …(1)

(Y + Z)/2 = 32

⇒ (Y + Z) = 64              …(2)

Also,

X + Y + Z = 5X

⇒ Y + Z = 4X

Substituting from (2),

⇒ 4X = 64

⇒ X = 16

⇒ Y = 46 – 16 = 30

⇒ Z = 64 – 30 = 34

∴ The numbers are 16, 30, 34

After 6 months, P doubled his investment.

⇒ P invested Rs. 3500 for 6 months and Rs. 7000 for other 6 months.

Q and R invested for only 4 months of the year.

The ratio of profits of P, Q, R and S

= (6 × 3500 + 6 × 7000) : (4 × 3500) : (4 × 3500) : (12 × 3500)

= 9 : 2 : 2 : 6

Q got a profit of Rs. 200.

So, total profit = ((9 + 2 + 2 + 6)/2) × Rs. 200 = Rs. 1900

To find which scheme will be beneficiary we should calculate interest governed by both schemes.

Interest earned by simple interest scheme-

Speed of each boat in still water = 8 km/hr

Suppose the speed of stream is v km/hr.

⇒ Speed of boat that goes upstream = (8 – v) km/hr

And, Speed of boat that goes downstream = (8 + v) km/hr

Suppose the boats meet after T hours.

We know, Distance = Speed × Time

⇒ Distance covered by boat moving upstream = (8 - v) km/hr × T hr = (8 - v)T km

⇒ Distance covered by boat moving downstream = (8 + v) km/hr × T hr = (8 + v)T km

Now, total distance covered by boats should be equal to 20 km.

⇒ (8 – v)T + (8 + v)T = 20

⇒ 16T = 20

⇒ T = 1.25 hours = 1 hour + (0.25 × 60 minutes) = 1 hour and 15 minutes

∴ Time taken for the boats to meet = 1 hour and 15 minutes