50 points question
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Answers
Answer:
Step-by-step explanation:
1). 3x+9-2x+2 = 5x-25
=> 3x-2x-5x = -25-9-2
=> -4x = -36
=> x = 36/4
=> x = 9
Check : 3(9+3) - 2(9-1) = 5(9-5)
=> 3(12) - 2(8) = 5(4)
=> 36-16 = 20
=> 20 = 20
2). Total length of Wire= Perimeter Of Rectangle
Let Its Breadth = 'x'
So Its Length = 'x+7'
Perimeter Of Rectangle= Total length of Wire [Perimeter = 2(l +b)]
2(x + x +7) = 86
2x + 7 = 86/2
2x + 7 = 43
2x = 43 -7
2x = 36
x = 18 cm
Therfore Breadth = 18cm
Length = x + 7
= 18 + 7
= 25 cm
3). Let, Reena's brother age be x years.
And Reena be x+6 years.
ATQ
=> 6+x+x=28
=> 2x=28-6
=> 2x=22
=> x=22/2
=> x=11
Therefore, Reena's brother age is 11 years Reena's age is 11+6=17 years.
4). Let Rahim was x years old 8 years back.
Rahim's age today will be x+8.
So rahim's age after 32 years will be x + 8 + 32 = x+40 -----1
And rahim's age after 32 years = 5x -----2
Equating 1 and 2,
=>x + 40 = 5x
=>4x = 40
=>x = 10
Rahim's age today is x+8
= 10+8
= 18 years
5). (A)
2m/3 - m/2 = -1-8
=> 4m-3m/6 = -9
=> m = -9*6
=> m = -54
Verify: 2(-54)/3 + 8 = -54/2 - 1
=> 2(-18)+8 = -27-1
=> -36+8 = -27-1
=> - 28 = -28
(B). 3(x-1) = 4(x-3)
=> 3x-3 = 4x-12
=> 3x-4x = -12+3
=> -x = -9
=> x = 9
Verify: 3/4(9-1) = 9-3
=> 3/4*8 = 6
=> 3*2 = 6
=> 6 = 6
6). Income = Rs 15300
Savings = Rs 1224
Ratio = 15300 / 1224 = 25 / 2 = 25 : 2
So, the ratio of of income and savings is 25 : 2.
Expenditure = Income - savings = 15300 - 1224 = Rs 14076
Ratio of Income and expenditure = 15300 / 14076
= 25 / 23 = 25 : 23
So, the ratio of expenditure and income is 25 : 23.
Ratio of expenditure and savings =
14076/1224
= 23 / 2
So, the ratio of expenditure and savings is 23:2.
Step-by-step explanation:
1). 3x+9-2x+2 = 5x-25
=> 3x-2x-5x = -25-9-2
=> -4x = -36
=> x = 36/4
=> x = 9
Check : 3(9+3) - 2(9-1) = 5(9-5)
=> 3(12) - 2(8) = 5(4)
=> 36-16 = 20
=> 20 = 20
2). Total length of Wire= Perimeter Of Rectangle
Let Its Breadth = 'x'
So Its Length = 'x+7'
Perimeter Of Rectangle= Total length of Wire [Perimeter = 2(l +b)]
2(x + x +7) = 86
2x + 7 = 86/2
2x + 7 = 43
2x = 43 -7
2x = 36
x = 18 cm
Therfore Breadth = 18cm
Length = x + 7
= 18 + 7
= 25 cm
3). Let, Reena's brother age be x years.
And Reena be x+6 years.
ATQ
=> 6+x+x=28
=> 2x=28-6
=> 2x=22
=> x=22/2
=> x=11
Therefore, Reena's brother age is 11 years Reena's age is 11+6=17 years.
4). Let Rahim was x years old 8 years back.
Rahim's age today will be x+8.
So rahim's age after 32 years will be x + 8 + 32 = x+40 -----1
And rahim's age after 32 years = 5x -----2
Equating 1 and 2,
=>x + 40 = 5x
=>4x = 40
=>x = 10
Rahim's age today is x+8
= 10+8
= 18 years
5). (A)
2m/3 - m/2 = -1-8
=> 4m-3m/6 = -9
=> m = -9*6
=> m = -54
Verify: 2(-54)/3 + 8 = -54/2 - 1
=> 2(-18)+8 = -27-1
=> -36+8 = -27-1
=> - 28 = -28
(B). 3(x-1) = 4(x-3)
=> 3x-3 = 4x-12
=> 3x-4x = -12+3
=> -x = -9
=> x = 9
Verify: 3/4(9-1) = 9-3
=> 3/4*8 = 6
=> 3*2 = 6
=> 6 = 6
6). Income = Rs 15300
Savings = Rs 1224
Ratio = 15300 / 1224 = 25 / 2 = 25 : 2
So, the ratio of of income and savings is 25 : 2.
Expenditure = Income - savings = 15300 - 1224 = Rs 14076
Ratio of Income and expenditure = 15300 / 14076
= 25 / 23 = 25 : 23
So, the ratio of expenditure and income is 25 : 23.
Ratio of expenditure and savings =
14076/1224
= 23 / 2
So, the ratio of expenditure and savings is 23:2