please answer this question
Answers
Puzzle - 1:-
Let Apple = A
Let Pomegranate = P
Let Mushroom = M
Now,
Given that
A+A+A+A = 28
=> 4A = 28
=> A = 28/4
=> A = 7
Each apple = 7
A × P = 21
=> 7×P = 21
=> P = 21/7
=> P = 3
Each Pomegranate = 3
P × M - A = 17
=> 3 × M - 7 = 17
=> 3 M - 7 = 17
=> 3 M = 17+7
=> 3 M = 24
=> M = 24/3
=> M = 8
Each Mushroom = 8
Now,
A × M + P - M
=> 7 × 8 + 3 - 8
=> 56+3-8
=> 59-8
=> 51
The value is 51
Puzzle - 2:-
Let the number be X
7 times of X = 7X
On adding 50 to it then it will be 7X+50
We know that
1 century = 100
3 centuries = 3×100 = 300
According to the given problem
7X+50+40 = 300
=> 7X+90 = 300
=> 7X = 300-90
=> 7X = 210
=> X = 210/7
=> X = 30
The required number is 30
Puzzle - 3:-
Given that
Radius of a circle = R
We know that
Area of a circle = π(radius)² sq.units
Area of the circle = πR² sq.units
Quarter = 1/4th of the circle
Area of the quarter of the circle = πR²/4 sq.units
Radius of the another circle = r units
Area of the circle = πr² sq.units
Area of the half of the circle = πr²/2 sq.units
According to the given problem
πR²/4 = πr²/2
=> R²/4 = r²/2
=> R² = 4r²/2
=> R² = 2r²
=> R = √(2r²)
=> R = √2 r
Now , The ratio of R and r
=> R:r = √2 r : r
=> √2 r / r
=> √2/1
=> √2 : 1
R:r = √2 : 1
Puzzle - 4:-
From the given figure,
We have
Radius of the circle = 28 m
The grazing field is the area of the sector of the circle whose angle is 90°
We know that
Area of a sector = (x°/360°)×πr² sq.units
Area of the grazing field
= (90°/360°)×(22/7)×28² m²
= (1/4)×(22/7)×28×28
= (1/4)×22×4×28
= 22×28
= 616 m²
Area of the field horse can graze is 616 m²
Puzzle - 5 :-
Let the number of people each team has be X
Total number of people in 16 teams = 16X
Number of people left in the semi final stage = 12
Semi final means 4 teams are left
Number of people in 4 teams = 4X
Therefore, 4X = 12
=> X = 12/4
=> X = 3
Number of people in each team = 3
Total number of people in 16 teams = 16X
=> 16×3 = 48
Total number of people entered the quiz = 48
( Semi finals = 4 teams
Finals = 2 teams
Winners = 1 team )
Answer:
Puzzle - 1:-
Let Apple = A
Let Pomegranate = P
Let Mushroom = M
Now,
Given that
A+A+A+A = 28
=> 4A = 28
=> A = 28/4
=> A = 7
Each apple = 7
A × P = 21
=> 7×P = 21
=> P = 21/7
=> P = 3
Each Pomegranate = 3
P × M - A = 17
=> 3 × M - 7 = 17
=> 3 M - 7 = 17
=> 3 M = 17+7
=> 3 M = 24
=> M = 24/3
=> M = 8
Each Mushroom = 8
Now,
A × M + P - M
=> 7 × 8 + 3 - 8
=> 56+3-8
=> 59-8
=> 51
The value is 51
Puzzle - 2:-
Let the number be X
7 times of X = 7X
On adding 50 to it then it will be 7X+50
We know that
1 century = 100
3 centuries = 3×100 = 300
According to the given problem
7X+50+40 = 300
=> 7X+90 = 300
=> 7X = 300-90
=> 7X = 210
=> X = 210/7
=> X = 30
The required number is 30
Puzzle - 3:-
Given that
Radius of a circle = R
We know that
Area of a circle = π(radius)² sq.units
Area of the circle = πR² sq.units
Quarter = 1/4th of the circle
Area of the quarter of the circle = πR²/4 sq.units
Radius of the another circle = r units
Area of the circle = πr² sq.units
Area of the half of the circle = πr²/2 sq.units
According to the given problem
πR²/4 = πr²/2
=> R²/4 = r²/2
=> R² = 4r²/2
=> R² = 2r²
=> R = √(2r²)
=> R = √2 r
Now , The ratio of R and r
=> R:r = √2 r : r
=> √2 r / r
=> √2/1
=> √2 : 1
R:r = √2 : 1
Puzzle - 4:-
From the given figure,
We have
Radius of the circle = 28 m
The grazing field is the area of the sector of the circle whose angle is 90°
We know that
Area of a sector = (x°/360°)×πr² sq.units
Area of the grazing field
= (90°/360°)×(22/7)×28² m²
= (1/4)×(22/7)×28×28
= (1/4)×22×4×28
= 22×28
= 616 m²
Area of the field horse can graze is 616 m²
Puzzle - 5 :-
Let the number of people each team has be X
Total number of people in 16 teams = 16X
Number of people left in the semi final stage = 12
Semi final means 4 teams are left
Number of people in 4 teams = 4X
Therefore, 4X = 12
=> X = 12/4
=> X = 3
Number of people in each team = 3
Total number of people in 16 teams = 16X
=> 16×3 = 48
Total number of people entered the quiz = 48
( Semi finals = 4 teams
Finals = 2 teams
Winners = 1 team )