answer these 5 questions with explanation correct and I will mark you brainliest
SCAMING WILL GET REPORTED
Answers
Answer:
1)
Let the number be in the form of 10x + y
A.T.Q.
x + y = 9. --------1
10x + y + 9 = 10y + x
10x - x + 9 = 10y - y
9x + 9 = 9y
x + 1 = y. ---------2
Putting y = x + 1 in equ.1
x + x + 1 = 9
2x + 1 = 9
2x = 8
x = 4
The number is 45.
2)
Let the numbers be x & y.
A.T.Q.
x + y = 5 ---------1
x^2 - y^2 = 5 ----------2
x - y = ?
Using equ. 1 & 2
x^2 - y^2 = 5 (x^2 - y^2 = (x + y)(x - y))
(x + y)(x - y) = 5
(5)(x - y) = 5
x - y = 1
3)
Let the numbers be in the form of x, x +1, x +2, x+3.
A.T.Q.
x + x + 1 + x + 2 + x + 3 = 166
4x + 6 = 166
4x = 160
x = 40
Therefore, the numbers are 40, 41, 42 & 43.
4)
x = x/2 + x/4 + 1200
x = 2x/4 + x/4 + 1200
x = 2x + x / 4 + 1200
x - 3x/4 = 1200
x/4 = 1200
x = ₹ 4800
5)
Perimeter = 2(l+b)
220 = 2(5y + 4 + 2y + 36)
110 = 7y + 40
7y = 70
y = 10
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Step-by-step explanation:
Solutions :-
1)
Let the two digits of a number be X and Y
Let the digit at 10's place = X
Let the digit at 1's place = Y
The two digit number = 10X+Y
Given that
The sum of the digits = 9
=> X+Y = 9
=>X = 9-Y -------(1)
If 9 is added to the number the digits interchanged
=> 10X+Y +9 = 10Y+X
=> 10X+Y+9-10Y-X = 0
=>9X-9Y +9 = 0
=> 9(X-Y+1) = 0
=> X-Y+1 = 0
=>9-Y-Y+1 = 0
=>10-2Y = 0
=> 2Y = 10
=> Y = 10/2
=> Y = 5
Now
X = 9-5 = 4
Therefore the number = 45
2)
Let the two numbers be X and Y
Sum of the two numbers = 5
=> X+Y = 5-----(1)
Difference of their squares = 5
=> X²-Y² = 5
=> (X+Y)(X-Y) = 5
=> 5(X-Y) = 5
=> X-Y = 5/5
=> X-Y = 1
The difference of the two numbers = 1
3)
Let the four consecutive natural numbers are X,X+1,X+2,X+3
Their sum = X+X+1+X+2+X+3 = 4X+6
According to the given problem
Their sum = 166
=> 4X+6 = 166
=> 4X = 166-6
=>4X = 160
=>X = 160/4
=> X = 40
X+1 = 40+1 = 41
X+2 = 40+2 = 42
X+3 = 40+3 = 43
The four consecutive natural numbers are 40,41,42,43
4)
Given that
Money of a man = Rs. X
Money given to his wife = half of the money
= Rs. X/2
Money given to his son = 1/4th of the money
=>Rs. X/4
Money given to his daughter = Rs. 1200
Total money
=> (X/2)+(X/4)+1200 = X
=> (2X+X+4800/4 = X
=> (3X+4800)/4 = X
=> (3X+4800) = 4X
=>4X=3X+4800
=>4X-3X = 4800
=>X = 4800
=>X-4800 = 0 is the required equation
=> X = 4800
The money of the man = Rs. 4800
5)
Length of the rectangle = (5y+4) cm
Breadth of the rectangle = (2y+36) cm
Perimeter of a rectangle = 2(l+b) units
=>P = 2(5y+4+2y+36) cm
=> P = 2(7y+40) cm
=> P = 14y+80 cm
According to the given problem
The perimeter = 220 cm
=> 14y+80 = 220
=> 14y = 220-80
=>14y = 140
=> y = 140/14
=> y = 10 cm
Therefore, the value of y = 10 cm