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The Correct Answer is: 15 litres

Explanation: 5 litres

Apply formula of allegation-

9/25 = ( 1- 6/X)² Or 3/5 = 1 – 6/x 6/X = 2/5 X (quantity of mixture)= 15 litres

The Correct Answer is: 36 days

Explanation:

Let total work = 36

efficiency of A = 3x B = 1x In 4 days, A did = 12x In 15 days, B did = 15x

Total work completed = 75% = 27

12x + 15x = 27 X = 1 B can do complete work in = 36/1 = 36 days

The Correct Answer is : 675√3/4 cm²

Lateral surface area = 3* (area of 1 equilateral triangle whose side is a)

Height of base triangle = √3a/2 √3a/2 * 2/3 = a/√3

a² = (5√6)² + (a/√3)² 2a²/3 = 150 a= 15 Side of triangle = 15 Area of 1 equilateral triangle = √3/4 * 15² = 225*√3/4

Area of lateral surface = area of 3 equilateral triangles = 3*225*√3/4 = 675√3/4 cm²

The Correct answer is:80kms

X/50 – X/60 = 16/60 X/300 = 16/60 X = 80 kms

The Correct Answer is: 102 yrs

Son = X Ram = 3x Father = 5*3x/2 = 7.5x

Average = (X+3x+7.5x)/3 = 11.5x/3 = 46

11.5x = 138 Sum of son and father = 8.5x = 138*8.5/115 = 138*17/23 = 102 years

The Correct Answer is: 46 yrs

Present age of daughter = X 3 yrs ago = x-3 Present age of Udit = 3x-9 Udit age 3 yrs ago = 3x -12 Mother’s present age = 2*(3x-12) = 6x -24

X + (3x -9) + (6x-24) = 107 X = 14

(6x -24) = 60 Difference b/w mother and daughter = 60-14 = 46 years

The Correct Answer is: 90 kmph

Let initial speed = 9x Speed after accident = 5x

150/5x – 150/9x = (12+2/9) – (10+8/9) 600/45x = 12/9 X = 10

So original speed = 9*10 = 90 kmph

The Correct Answer is: 16/3

8*( 1- cos²@) + 2√3.cos@ = 5 8cos²@ – 2√3cos@ – 3 = 0 8cos²@ – 4√3cos@ + 2√3cos@ – 3 = 0 4cos@(2cos@ – √3) + √3 ( 2cos@ – √3) = 0 2cos@ – √3 = 0 Cos@ = √3/2 So @ = 30°

Sec²30° + cosec²30 = 4/3 + 4 = 16/3

The Correct Answer is: (66 + 33√3)/4

Sin²75 + 2tan²75 + 2 {( √3+1)/2√2}² + 2*{(√3+1)/(√3-1)}² + 2 = (4+2√3)/8 + 2*(2+√3)² + 2 = (4+2√3)/8 + 16 + 8√3 = (4 + 128 + 2√3 + 64√3)/8 = (66 + 33√3)/4

The Correct Answer is: 7:1

Exterior angle = 21+ 3/17 = 360/17 Number of sides = 360/(360/17) = 17

Number of diagonals = 17*(17-3)/2 = 17*7

Ratio = 17*7: 17 = 7:1

## Ravi

This answer was edited.The Correct Answer is: 15 litres

Explanation: 5 litres

Apply formula of allegation-

9/25 = ( 1- 6/X)²

Or 3/5 = 1 – 6/x

6/X = 2/5

X (quantity of mixture)= 15 litres

## Ravi

The Correct Answer is: 36 days

Explanation:

Let total work = 36

efficiency of A = 3x

B = 1x

In 4 days, A did = 12x

In 15 days, B did = 15x

Total work completed = 75% = 27

12x + 15x = 27

X = 1

B can do complete work in = 36/1 = 36 days

## Ravi

The Correct Answer is : 675√3/4 cm²

Explanation:

Lateral surface area = 3* (area of 1 equilateral triangle whose side is a)

Height of base triangle = √3a/2

√3a/2 * 2/3 = a/√3

a² = (5√6)² + (a/√3)²

2a²/3 = 150

a= 15

Side of triangle = 15

Area of 1 equilateral triangle = √3/4 * 15² = 225*√3/4

Area of lateral surface = area of 3 equilateral triangles = 3*225*√3/4 = 675√3/4 cm²

## Ravi

The Correct answer is:80kms

Explanation:

X/50 – X/60 = 16/60

X/300 = 16/60

X = 80 kms

## Ravi

The Correct Answer is: 102 yrs

Explanation:

Son = X

Ram = 3x

Father = 5*3x/2 = 7.5x

Average = (X+3x+7.5x)/3 = 11.5x/3 = 46

11.5x = 138

Sum of son and father = 8.5x = 138*8.5/115 = 138*17/23 = 102 years

## Ravi

The Correct Answer is: 46 yrs

Explanation:

Present age of daughter = X

3 yrs ago = x-3

Present age of Udit = 3x-9

Udit age 3 yrs ago = 3x -12

Mother’s present age = 2*(3x-12) = 6x -24

X + (3x -9) + (6x-24) = 107

X = 14

(6x -24) = 60

Difference b/w mother and daughter = 60-14 = 46 years

## Ravi

The Correct Answer is: 90 kmph

Explanation:

Let initial speed = 9x

Speed after accident = 5x

150/5x – 150/9x = (12+2/9) – (10+8/9)

600/45x = 12/9

X = 10

So original speed = 9*10 = 90 kmph

## Ravi

The Correct Answer is: 16/3

Explanation:

8*( 1- cos²@) + 2√3.cos@ = 5

8cos²@ – 2√3cos@ – 3 = 0

8cos²@ – 4√3cos@ + 2√3cos@ – 3 = 0

4cos@(2cos@ – √3) + √3 ( 2cos@ – √3) = 0

2cos@ – √3 = 0

Cos@ = √3/2

So @ = 30°

Sec²30° + cosec²30 = 4/3 + 4 = 16/3

## Ravi

The Correct Answer is: (66 + 33√3)/4

Explanation:

Sin²75 + 2tan²75 + 2

{( √3+1)/2√2}² + 2*{(√3+1)/(√3-1)}² + 2

= (4+2√3)/8 + 2*(2+√3)² + 2

= (4+2√3)/8 + 16 + 8√3

= (4 + 128 + 2√3 + 64√3)/8

= (66 + 33√3)/4

## Ravi

The Correct Answer is: 7:1

Explanation:

Exterior angle = 21+ 3/17 = 360/17

Number of sides = 360/(360/17) = 17

Number of diagonals = 17*(17-3)/2 = 17*7

Ratio = 17*7: 17 = 7:1