Linear Equation
- Smita was asked to multiply a certain number by 36. She multiplied it by 63 instead and got an answer of 3834 more than the correct one. What was the number to be multiplied?
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Let us assume the certain Number is A.
According to question,
63A = 3834 + 36A
Solve the equation.Correct Option: C
Let us assume the certain Number is A.
According to question,
63A = 3834 + 36A
63A - 36A = 3834
⇒ 27A = 3834
⇒ A = 142
- The ratio of two numbers is 4:7. If each of those numbers increased by 30, their ratio will become 5:8 . What is the average of these two numbers ?
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Let the numbers be x and y.
According to question,
The ratio of two numbers is 4:7.
⇒ x/y = 4/7
⇒ 7x = 4y
∴ 7x - 4y = 0 ........................(1)
Again According to question,
If each of those numbers increased by 30, their ratio will become 5:8
(x + 30) / (y + 30) = 5/8
⇒ 8(x + 30) = 5(y + 30)
⇒ 8x + 240 = 5y + 150
⇒ 8x - 5y = -90 ..........................(2)
Multiply 5 with equation (1) , we will get.
35x - 20y = 0 ..................(3)
Multiply 4 with equation (2), we will get.
32x - 20y = -360 ............(4)
Subtracts the Equation (4) from Equation (3). we will get,
Solve the equation and get the answer.Correct Option: D
Let the numbers be x and y.
According to question,
The ratio of two numbers is 4:7.
⇒ x/y = 4/7
⇒ 7x = 4y
∴ 7x - 4y = 0 ........................(1)
Again According to question,
If each of those numbers increased by 30, their ratio will become 5:8
(x + 30) / (y + 30) = 5/8
⇒ 8(x + 30) = 5(y + 30)
⇒ 8x + 240 = 5y + 150
⇒ 8x - 5y = -90 ..........................(2)
Multiply 5 with equation (1) , we will get.
35x - 20y = 0 ..................(3)
Multiply 4 with equation (2), we will get.
32x - 20y = -360 ............(4)
Subtracts the Equation (4) from Equation (3). we will get,
35x - 20y - (32x - 20y) = 0 - (-360)
⇒ 35x - 20y - 32x + 20y = 360
⇒ 3x = 360
⇒ x = 120
Put the value of x in equation (1) to get the value of y.
7x - 4y = 0
⇒ 7(120) - 4y = 0
⇒ 840 - 4y = 0
⇒ 4y = 840
⇒ y = 210
∴ Average of the numbers = (x + y)/2
put the vale of x and y.
∴ Average of the numbers = (120 + 210)/2
∴ Average of the numbers = 330/2
∴ Average of the numbers = 165
- The ratio of the present ages of a mother and daughter is 7:1 . Four years ago the ratio of their ages was 19:1 . What will be the mother's age four years from now ?
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Method 1
Let us assume the present age of mother be M and daughter be D.
According to question,
Ratio of present age of mother and daughter = 7 : 1
M / D = 7 : 1
⇒ M / D = 7 / 1
⇒ M / D = 7
⇒ M = 7D ..........................(1)
Four years ago the age of mother = M - 4
Four years ago the age of daughter = D - 4
Again according to question,
Four years ago ratio of mother age and daughter age = 19 : 1
⇒ (M - 4 ) / (D - 4) = 19 : 1
⇒ (M - 4 ) / (D - 4) = 19
⇒ (M - 4 ) = 19(D - 4)
⇒ M - 4 = 19D - 76 .....................(2)
Solve the above equation to get the answer.
Method 2
Let us assume the ratio factor is x.
According to question,
Ratio of present age of mother and daughter = 7 : 1
Then present age of mother = 7x and present age of daughter = x
Four years ago the age of mother = 7x - 4
Four years ago the age of daughter = x - 4
Again according to question,
Four years ago ratio of mother age and daughter age = 19 : 1
Solve the above equation.Correct Option: C
Method 1
Let us assume the present age of mother be M and daughter be D.
According to question,
Ratio of present age of mother and daughter = 7 : 1
M / D = 7 : 1
⇒ M / D = 7 / 1
⇒ M / D = 7
⇒ M = 7D ..........................(1)
Four years ago the age of mother = M - 4
Four years ago the age of daughter = D - 4
Again according to question,
Four years ago ratio of mother age and daughter age = 19 : 1
⇒ (M - 4 ) / (D - 4) = 19 : 1
⇒ (M - 4 ) / (D - 4) = 19
⇒ (M - 4 ) = 19(D - 4)
⇒ M - 4 = 19D - 76 .....................(2)
Put the value of M from equation (1) in above equation (2), we will get
7D - 4 = 19D - 76
⇒ 76 - 4 = 19D - 7D
⇒ 72 = 12D
⇒ 12D = 72
⇒ D = 72/12
⇒ D = 6
Put the vale of D in equation (1), we will get the present age of mother.
Present age of Mother M = 7D = 7 x 6
Present age of Mother M = 42
∴ mother's age after 4 yrs = 42 + 4 = 46 yrs
Method 2
Let us assume the ratio factor is x.
According to question,
Ratio of present age of mother and daughter = 7 : 1
Then present age of mother = 7x and present age of daughter = x
Four years ago the age of mother = 7x - 4
Four years ago the age of daughter = x - 4
Again according to question,
Four years ago ratio of mother age and daughter age = 19 : 1
⇒ (7x - 4 ) / (x - 4) = 19 : 1
⇒ (7x - 4 ) / (x - 4) = 19
⇒ (7x - 4 ) = 19(x - 4)
⇒ 7x - 4 = 19x - 76
⇒ 76 - 4 = 19x - 7x
⇒ 72 = 12x
⇒ 12x = 72
⇒ x = 6
Present age of Mother = 7x = 7 x 6 = 42
∴ mother's age after 4 yrs = 42 + 4 = 46 yrs
- Ravi has spent a quarter (1/4) of his life as a boy , one fifth (1/5) as a youth , one third (1/3) as a man and thirteen (13) years in old age . What is his present age ?
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Suppose that the Ravi present age is A years.
According to the given question,
A/4 + A/5 + A/3 + 13 = A
Solve the above equation to find the answer.Correct Option: C
Suppose that the Ravi present age is A years.
According to the given question,
A/4 + A/5 + A/3 + 13 = A
⇒ (15A + 12A + 20A)/60 = A - 13
⇒ 47A = 60A - 780
⇒60A - 47A = 780
⇒13A = 780
∴ A = 780/13 = 60 years
- A number of two digits has 3 for its unit's digit, and the sum of digits is 1/7 of the number itself, The number is
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Let the ten's digit be x. Then, number = 10x + 3 and sum of digits = ( x + 3 )
So ,(x+3) = 1/7(10x + 3)
⇔ 7x + 21 = 10x + 3
⇔ 3x = 18
⇔ x=6
Hence, the number = 10x + 3 = (10 x 6) + 3 = 63.Correct Option: C
Let the ten's digit be x. Then, number = 10x + 3 and sum of digits = ( x + 3 )
So ,(x+3) = 1/7(10x + 3)
⇔ 7x + 21 = 10x + 3
⇔ 3x = 18
⇔ x=6
Hence, the number = 10x + 3 = (10 x 6) + 3 = 63.
