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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, and in the bracket, the BODMAS rule must be followed,

?% of (40% of 1500) = (60% of 20)% of 750

⇒ ?% of (40/100 × 1500) = (60/100 × 20)% of 750

⇒ ?% of 600 = 12% of 750

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

⇒ ?/100 × 600 = 12/100 × 750

⇒ ? = 90/6

∴ ? = 15

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 and in the bracket,

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.

Given expression is,

21.80% of 700 + 65.74 = 169.14 + ? % of 300.10

We can write the given values as:

21.80 ≈ 22 and 65.74 ≈ 66

169.14 ≈ 169 and 300.10 ≈ 300

Then,

⇒ 22% of 700 + 66 = 169 + ?% of 300

⇒ (22/100) × 700 + 66 = 169 + (?/100) × 300

⇒ 22 × 7 + 66 = 169 + (3 × ?)

⇒ 154 + 66 = 169 + (3 × ?)

⇒ 220 = 169 + (3 × ?)

⇒ (3 × ?) = 220 - 169

⇒ 3 × ? = 51

⇒ ? ≈ 17

√5041 × 61.67 × (2.98/17.89) ÷ ³√215 = ?^1/3 + 45.48

It can be approximated as √5041 × 62 × (3/18) ÷ ³√216 = ?^1/3 + 46

 71 × 62 × (1/6) × 1/6 = ?^1/3 + 46

4402/36 = ?^1/3 + 46

?^1/3= 122.27 – 46

? = 76.27³

(80.0003% of 1601.73) + (75.123% of 1003.158) + 1000 - (50.82% of 3001.72) × 2.0007

Concept used:

Calculation:

⇒ (80% of 1600) + (75% of 1000) + 1000 - (50% of 3000) × 2,

⇒ (80 × 16) + (75 × 10) + 1000 - (50 × 30) × 2, (Simplifying ‘brackets’)

⇒ 1280 + 750 + 1000 - 1500 × 2,

⇒ 3030 - 3000,

⇒ 30

∴ ? = 30

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, and in the bracket,

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.

Given expression is,

98.8 × 4032 ÷ 27.89% of 599 = 16 × 339.7 ÷ 17.2 + ? + 80.1

Taking Approximate values as,

98.8 ≈ 99, 27.89 ≈ 28, 599 ≈ 600, 339.7 ≈ 340, 17.2 ≈ 17, 80.1 ≈ 80

⇒ 99 × 4032 ÷ 28% of 600 = 16 × 340 ÷ 17 + ? + 80

⇒ 99 × 4032 ÷ 0.28 × 600 = 16 × 20 + ? + 80

⇒ 99 × 24 = 320 + ? + 80

∴ ? = 2000

Given,

⇒ [{(1948 + 652 – 140) ÷ (41 × 8)} + (313 ÷ 2)] = 2⁶ + 10^?

⇒ [{(2600 – 140) ÷ (41 × 8)} + (313 ÷ 2)] = 2⁶ + 10^?

⇒ [{2460 ÷ (41 × 8)} + (313 ÷ 2)] = 2⁶ + 10^?

⇒ [{2460 ÷ 328} + (313 ÷ 2)] = 2⁶ + 10^?

⇒ [7.5 + 156.5] = 2⁶ + 10^?

⇒ 164 = 2⁶ + 10^?

⇒ 164 = 64 + 10^?

⇒ 10^? = 100

⇒ 10^? = 10²

⇒ ? = 2

Formula used:

(a – b) (a + b) = a² – b²

Calculations:

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, and following BODMAS rule in the bracket -

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 the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

 

Given expression is  :

( √7 + 2) ( √28 – 4 ) ( 3 + √5 ) ( 6 – √20 )    

⇒ ( √7 + 2) (2( √7 – 2 ))  ( 3 + √5 ) (2( 3 – √5 ))

⇒ 4 × ( √7 + 2) ( √7 – 2 ) ( 3 + √5 ) ( 3 – √5 )

⇒ 4 × (7 – 4)(9 – 5)

⇒ 4 × 3 × 4

 ∴ 48

Given, the speed of boat in still water is 6 km/hour

And the speed of stream is 2 km/hour

⇒ The speed of stream in downstream = 8 km/hour

And the speed of stream in upstream = 4 km/hour

Let the fixed distance be x km

Now, according to question

x/4 = 3 + x/8

⇒ x/4 – x/8 = 3

⇒ x/8 = 3

⇒ x = 24

⇒ The total distance covered by the boat in upstream and downstream = 24 × 2

∴ The total distance is 48 km

Shortcut Trick

The difference in the interest earned in three years on a certain sum P at R% p.a. (compounded annually and simple interest) = $\frac{PR^2}{100^2} \times (\frac{R}{100} + 3)$

According to the question,

⇒ ₹197.12 = $\frac{P(8)^2}{100^2} \times (\frac{8}{100} + 3)$

⇒ ₹197.12 = $\frac{64P}{10000} \times (\frac{308}{100})$

⇒ P = ₹10,000

 The principal invested is ₹10,000.

Alternate Method

Given:

A certain amount P is invested in scheme A for 3 years at a simple interest of 8% per annum.

The same amount P is invested in scheme B for 3 years at 8% per annum compounded annually.

The difference in the interest earned is ₹197.12.

Formula used:

(1) S.I = $\frac{P \times R \times T}{100}$

(2) C.I = P[(1 + $\frac{R}{100}$)T - 1]

Where, 

P, is the principal invested

R, rate of interest applied

T, is the time of investment 

S.I, is the simple interest earned

C.I, is the compound interest earned

Calculation:

Let P is the principal invested.

Let S.I is the simple interest earned.

Let C.I is the compound interest earned.

In the first case:

⇒ S.I = $\frac{P× 8 × 3}{100}$    ----(1)

In the second case:

⇒ C.I = P[(1 + $\frac{8}{100}$)³ - 1]

⇒ C.I = P[($\frac{27}{25}$)3 - 1]    ----(2)

According to the question,

⇒ C.I - S.I = P[($\frac{27}{25}$)3 - 1] - $\frac{P× 8 × 3}{100}$

⇒ ₹197.12 = P[$\frac{19683}{15625}$ - 1] - $\frac{P× 8 × 3}{100}$

⇒ ₹197.12 = P[$\frac{4058}{15625}$] - $\frac{24P}{100}$

⇒ ₹197.12 = P[$\frac{4058-3750}{15625}$]

⇒ P = ₹10,000

∴ The principal invested is ₹10,000.

Shortcut Trick

Time to cross platform (Train + Platform) = 30 seconds

Time to cross standing pole (Train only) = 10 seconds

Time taken to cover platform length alone = 30 − 10 = 20 seconds

Ratio of Train length to Platform length = 10 : 20 = 1 : 2

If 2 units = 300 m, then 1 unit = 150 m

∴ The correct answer is 150 m.

Alternate Method

Given: Length of platform = 300 m, Time to cross pole = 10 s, Time to cross platform = 30 s.

Formula Used: Speed = Distance ÷ Time

⇒ Speed of train (v) = Train Length (L) ÷ 10

⇒ Speed of train (v) = (L + 300) ÷ 30

⇒ L ÷ 10 = (L + 300) ÷ 30

⇒ 3 × L = L + 300

⇒ 2 × L = 300

⇒ L = 150 m

∴ The correct answer is 150 m.

Additional Information

Relative Speed

When two objects move in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Train Crossing Objects

To cross a point object (pole, man), distance = length of train. To cross a stationary object with length (bridge, tunnel, platform), distance = length of train + length of object.

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.