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Given:

Expenditure on medical = 15% of his income

Expenditure on traveling = 25% of his income

The expenditure left = Rs.2400

Calculation:

Let the total income be 100%

The left expenditure = 100% – (15% + 25%)

⇒ 100% – 40%

⇒ 60%

Now,

By using unitary method

60% = 2400

⇒ 1% = 2400/60

⇒ 1% = 40

⇒ 100% = 100 × 40

⇒ 100% = 4000

∴ The total income of person will be Rs.4000

Calculation:
\(\frac{{4x\space -\space 3}}{{x\space -\space 3}} = \; - \frac{1}{2}\) 
⇒ (4x – 3) × 2 = -1 × (x – 3)
⇒ 8x – 6 = -x + 3
⇒ 8x + x = 3 + 6
⇒ 9x = 9
⇒ x = 1
∴ The value of x is 1.

Given:

ba = 50625

Calculation:

50625 = 3 × 3 × 3 × 3 × 5 × 5 × 5 × 5 

b^a = (15)⁴

∴ b = 15 and a = 4

Now, (b - 1)b + a - 2 

⇒ (15 - 1)^{15 + 4 - 2}

⇒ 14^{19 - 2}

⇒ 14¹⁷ 

Given∶

[49ⁿ⁺¹(7^n/2)^-2 – 343ⁿ]/[(2 × 7^m)³ × 6] = 1/117649

Calculation∶

[49ⁿ⁺¹(7^n/2)^-2 – 343ⁿ]/[(2 × 7^m)³ × 6] = 1/117649

⇒ [{(7²)^{n + 1}} × (7^{(-n/2) × (-2)}) – (7³)ⁿ]/[2³ × 7^3m × 6] = 1/7⁶

⇒ [7²ⁿ.7².7ⁿ- 7³ⁿ]/[2³ × 7^3m × 6] = 1/7⁶

⇒ [7³ⁿ.7² – 7³ⁿ]/[2³ × 7^3m × 6] = 1/7⁶

⇒ [7³ⁿ (7² – 1)]/[48 × 7^3m] = 1/7⁶

⇒ [7³ⁿ × 48]/[48 × 7^3m] = 1/7⁶

⇒ 7^{3n - 3m} = 7^-6

⇒ 3n - 3m = -6

⇒ 3(n - m) = -6

⇒ (n - m) = -2

⇒ m - n = 2

∴ The required value is 2.

Let the total no of mangoes in the crate be x 

Then the no of bruised mango = 1/30 x

Let the no of unsalable mangoes =3/4 (1/30 x) 

1/40 x =12 

x = 480

Given:

\(\frac {0.325 × 0.325 + 0.175 × 0.175 - 25 × 0.00455}{5 × 0.0065 × 3.25 - 7 × 0.175 × 0.025} \)

Calculations:

[(0.325)² + (0.175)² - 25 × 0.0045]/[5 × 0.0065 - 7 × 0.025 × 0.175]

⇒ [(0.325)² + (0.175)² - 0.11375]/[0.10563 - 0.03063]

⇒ (0.015)²/0.075 = 0.0225/0.075

⇒ 0.3

∴The required value is 0.3

Given:

At the beginning

J and B together had four times as T

T and B together had three times as J

At the end

J and B together had three times as T 

T and B together had two times as J

B lost Rs.200

Calculation:

let the total amount J + B+ T = x

At the beginning

J + B = 4T     

the total amount with them = 5T ⇒  x

⇒ T = (1/5)x      ----(I)

T + B = 3J      

Total amount = 4J ⇒ x

⇒ J = (1/4)x      ----(II)

At the end 

J + B = 3T    

total amount = 4T ⇒  x 

⇒ T = (1/4)x     ----(iii)

T + B = 2J

total amount = 3J ⇒ x 

⇒ J = (1/3)x   ----(iv)

Taking LCM for T and J at the beginning and at the end,

from (I), (ii), (iii), (iv)

T & J = (1/5, 1/4),(1/4,1/3) 

LCM = 60 then,

At beginning

T = 12 , J = 15

At end 

T = 15, J = 20 

The difference in value of J at the end and at the beginning

J = 20 - 15 ⇒ 5 

here the value is increased at end from beginning so he won

fraction = 5/60 ⇒ 1/12

∴  J win 1/12 of the total money 

Concept used:

a² - b² = (a + b)(a - b)

Calculation:

 \(\frac{7+3√5}{3+√5}-\frac{7-3√5}{3-√{5}}\)

⇒ \( ((7+3√5)(3- √5)- (7-3√5)(3+ √5))/(3+ √5)(3- √5) \)

⇒ (21 + 9√5 - 7√5 - 15 - 21 + 9√5 - 7√5 + 15)/4

⇒ 4√5/4 = √5

(∵ √5 = 2.236 approx)

⇒ 2.3 (approx)

∴ The value lies between 2 and 2.5.

Given:

x = 113 + 11.3 + 1.13 + 0.113 + 0.0113 

Calculations:

⇒ 113.0000 + 11.3000 + 1.1300 + 0.1130 + 0.0113

⇒ 124.3000 + 1.1300 + 0.1130 + 0.0113

⇒ 124.3000 + 1.2543

⇒ 125.5543

∴ The value is 125.5543.

Calculations:

Considering the given equation,

(27)2 – (13)2 + (12)3 + (23)2 = ?

⇒ 729 – 169 + 1728 + 529 = ?

⇒ 2817 = ?

∴ The value of ? is 2817.

Concept:

√(a/b) =  (√a/√b)

Calculations:

√(7/5) = (√7/√5)

Multiplying by √5 in numerator and denominator, we get        

⇒ ((√7×√5)/(√5×√5))

⇒ (√35/5)

given that, √35 = 5.9160

⇒ 5.9160/5 = 1.1832  

Given

37% of 150 - 0.05 % of 1000 = A

Calculation

37 × (1/100) × 150 - 0.05 × (1/100) × 1000

⇒ 37 × 3/2 - 0.05 × 10

⇒ 55.5 - 0.5

⇒ 55

Given:

Half of thrice of a number = 60%

Calculation:

Let assume that number is x

Thrice of a number = 3x

Half of thrice of a number  = ½ × 3x = 3x/2

According to question

⇒ 3x/2 = 60/100

By cross multiplication

⇒ x = (60/100) × (2/3)

⇒ x = 2/5

∴ That number is 2/5.

The correct option is 4 i.e. 2/5

Given:

We have to find the value of 15% of 60% of 1,000

Concept Used:

Percentage to Fraction Conversion

Calculation:

15% of 60% of 1,000

⇒ 15% × 60% × 1,000

⇒ 3/20 × 3/5 × 1,000

⇒ 3 × 3 × 10

⇒ 90

∴ The required value of 15% of 60% of 1,000 is 90.

Calculations:

Let the number added be x.

15% of 180 + x = 20% of 360

⇒ 180 × (15/100) + x = 360 × (20/100)

⇒ 27 + x = 72

⇒ x = 72 - 27 = 45

∴ The number to be added is 45.

Given:

\(1\frac{3}{4} + 5\frac{1}{3} + 3\frac{2}{5}\)

Calculation:

7/4 + 16/3 + 17/5

Taking L.C.M

⇒ (105 + 320 + 204)/60

⇒ 629/60 = \(10\frac{{29}}{{60}}\)

∴ The value of ? is \(10\frac{{29}}{{60}}\)

Given:

\(\frac{n^2+6n-72}{n-6}\)

Concept used:

Simplification

Calculation:

⇒ \(\frac{{{n^2} + 12n - 6n - 72}}{{n - 6}}\)

⇒ \(\frac{{n\left( {n + 12} \right) - 6\left( {n + 12} \right)}}{{n - 6}}\)

⇒ \(\frac{{\left( {n + 12} \right)\left( {n - 6} \right)}}{{n - 6}}\)

∴ n + 12

Given:

83 ÷ 24 + 5² × 7² – (22)3 = ?

Concept used:

a^x/a^y = a^{x – y}

(a^x)^y = a^{x × y}

a^x × b^x = (a × b)^x

Calculations:

Using the given concept to solve the equation,

⇒ [(2³)3 ÷ 2⁴] + (5 × 7)² – 4³ 

⇒ (2⁹/2⁴) + 35² – 64

⇒ 2⁵ + 1225 – 64

⇒ 32 + 1225 – 64

⇒ 1225 – 32

⇒ 1193

∴ 1193 will replace the question mark in the given question

Given: 

25% of 84 × 24% of 85 

Concept used:

a% of N = (a/100) × N

where N and a are natural number 

Calculation:

25% of 84 × 24% of 85 

⇒ (25/100) × 84 × (24/100) × 85 

⇒ (84/4) × (102/5)  

⇒ (21 × 102)/5 = 428.4

∴ The value of '?' is 428.4

Concept:

This type of question can be solved by the help of BODMAS

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.

Calculation:

12.5% of 48 – 5 + 50% of 34 = ?

⇒ (1/8) × 48 – 5 + (1/2) × 34

⇒ 6 – 5 + 17

⇒ 23 – 5

⇒ 18

∴ The required result will be 18.

Concept:

This type of question can be solved by the help of BODMAS

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.

Calculation:

12 – 25% of 28 – 2 = ?

⇒ 12 – 7 – 2

⇒ 5 – 2

⇒ 3

∴ The required result will be 3.

Concept:

This type of question can be solved by the help of BODMAS

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.

Calculation:

30% of 30 – 12 + 7 = ?

⇒ 9 – 12 + 7

⇒ 16 – 12

⇒ 4

∴ The required result will be 4.

Given:

2x - 1 + 2x + 1 = 320. We have to find the value of x.

Calculation:

2x - 1 + 2x + 1 = 320

⇒ 2^x/2 + 2^x × 2 = 320

⇒ 2^x(1/2 + 2) = 320

⇒ 2^x × (5/2) = 320

⇒ 2^x = 320 × (2/5)

⇒ 2^x = 64 × 2

⇒ 2^x = 128

⇒ 2^x = 2⁷

⇒ x = 7

∴ The required value of x is 7.

Given:

We have to simplify \({{0.8 × 0.8 × 0.8} - {0.7 × 0.7 × 0.7}} \over {(0.8)^2 + (0.7)^2 + 0.56}\)

Concept Used:

a³ - b³ = (a - b) × (a² + ab + b²)

Calculation:

\({{0.8 \times 0.8 \times 0.8} - {0.7 \times 0.7 \times 0.7}} \over {(0.8)^2 + (0.7)^2 + 0.56}\)

⇒ \({(0.8)^3 - (0.7)^3} \over {(0.8)^2 + (0.7)^2 + (0.7) \times (0.8)}\)

⇒ \({(0.8 - 0.7) \times [(0.8)^2 + (0.7)^2 +(0.8) \times (0.7)]} \over {(0.8)^2 + (0.7)^2 + (0.7) \times (0.8)}\)

⇒ (0.8 - 0.7)

⇒ 0.1

∴ The required simplified value is 0.1