Linear Equation
- A series of books was published at seven years interval. When the seventh book was issued, the sum of the publication year was 13,524. When was the first book published ?
-
View Hint View Answer Discuss in Forum
Let us assume the first book published in year x.
According to question,
Books are published at seven years interval,
First edition book published in year = x
When the seventh book was issued, the sum of the publication year was 13,524.
x + x + 7 + x +14 + x +21 + x + 28 + x + 35 + x + 42 =13524
Solve the equation.Correct Option: C
Let us assume the first book published in year x.
According to question,
Books are published at seven years interval,
First edition book published in year = x
Second edition book published in year = x + 7
Third edition book published in year = x + 14
Four edition book published in year = x + 21
Five edition book published in year = x + 28
Six edition book published in year = x + 35
Seven edition book published in year = x + 42
When the seventh book was issued, the sum of the publication year was 13,524.
x + x + 7 + x +14 + x +21 + x + 28 + x + 35 + x + 42 =13524
147 + 7x = 13524
7x = 13524 -147
⇒ x = 13377/7 = 1911
The first book published in year x = 1911
- The cost of 2 sarees and 4 shirts is ₹ 16000 while 1 saree and 6 shirts cost the same. The cost of 12 shirts is
-
View Hint View Answer Discuss in Forum
Let cost of one saree and shirt be x and y, respectively.
2x + 4y = 16000 ....(i)
x + 6y = 16000 ....(ii)
Solve above equations and find y
And finally cost of 12 shirts = 12yCorrect Option: B
Let cost of one saree and shirt be x and y, respectively.
2x + 4y = 16000 ....(i)
x + 6y = 16000 ....(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i). we get
2x + 4y = 16000
2x + 12y = 32000
-------------------------
-8y = -16000
∴ y = 2000
Putting the value of y in Eq. (ii), we get
x +6 x 2000 = 16000
∴ x = 4000
∴ Cost of 12 shirts = 12y
= 12 x 2000 = ₹ 24000
- If the number obtained on the interchanging the digits of two-digits number is 18 more than the original number and the sum of the digits is 8, then what is the original number ?
-
View Hint View Answer Discuss in Forum
Method 1 to solve the given question.
Lets assume the unit's digit is y and the ten's digit is x. then, the number is 10 x + y.
According to question, after interchanging the digits, the new number is 10y + x.
Then,
New Number - 18 = Original number
10y + x = 10x + y + 18
⇒ 9y - 9x = 18
⇒ y - x = 2 .....................(1)
Again according to question,
Sum of digits of Original Number = 8
x + y = 8 ..............................(2)
Solve the equation and get the answer.
Method 2 to solve the given question.
Given that sum of digits of original number is 8.
Let us assume that unit digit is x , then ten digit will be 8 - x. (since sum of digits is 8.)
Now Original number = 10( 8 - x) + x
After interchanging the digits , the number = 10x + (8 - x) = 9x + 8
According to question.
New number = original number + 18
⇒ 9x + 8 = 10(8 - x) + x + 18
Solve the equation and get the answer.Correct Option: C
Method 1 to solve the given question.
Lets assume the unit's digit is y and the ten's digit is x. then, the number is 10 x + y.
According to question, after interchanging the digits, the new number is 10y + x.
Then,
New Number - 18 = Original number
10y + x = 10x + y + 18
⇒ 9y - 9x = 18
⇒ y - x = 2 .....................(1)
Again according to question,
Sum of digits of Original Number = 8
x + y = 8 ..............................(2)
Add the equation (1) and (2) , we will get
y - x + x + y = 2 + 8
⇒ 2y = 10
⇒ y = 5
Put the value of Y in equation (2) , we will get
x + 5 = 8
⇒ x = 8 - 5 = 3
Then , the original number = 10x + y
Put the value of x and y and get the original number.
The original number = 10x + y = 10 x 3 + 5 = 30 + 5 = 35
Method 2 to solve the given question.
Given that sum of digits of original number is 8.
Let us assume that unit digit is x , then ten digit will be 8 - x. (since sum of digits is 8.)
Now Original number = 10( 8 - x) + x
After interchanging the digits , the number = 10x + (8 - x) = 9x + 8
According to question.
New number = original number + 18
⇒ 9x + 8 = 10(8 - x) + x + 18
⇒ 9x + 8 = 80 - 10x + x + 18
⇒ 9x + 8 = 98 - 9x
⇒ 9x + 9x = 98 - 8
⇒ 18x = 90
⇒ x = 90/18
⇒ x = 5
The original number = 10(8 - x) + x = 10(8 - 5) + 5 = 10(3) + 5 = 30 + 5 = 35
- A fraction becomes 7/8, if 5 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 6/7. Find the fraction.
-
View Hint View Answer Discuss in Forum
Let the fraction be x/y,
According to the question,
(x + 5) / (y + 5) = 7/8
⇒ 8x + 40 = 7x + 35
∴ 8x - 7y = -5 ..(i)
Again, according to the question,
(x + 3)/(y + 3) = 6/7
⇒ 7x + 21 = 6y + 18
∴ 7x - 6y = -3 ..(ii)Correct Option: B
Let the fraction be x/y,
According to the question,
(x + 5) / (y + 5) = 7/8
⇒ 8x + 40 = 7x + 35
∴ 8x - 7y = -5 ..(i)
Again, according to the question,
(x + 3)/(y + 3) = 6/7
⇒ 7x + 21 = 6y + 18
∴ 7x - 6y = -3 ..(ii)
On multiplying Eq. (i) by 6 and Eq. (ii) by 7 and subtracting, we get
48x - 42y = -30
49x - 42y = -21
---------------------
-x = -9
∴ x = 9
On putting te value of x in Eq. (i) , we get
72 - 7y = -5
⇒ -7y = -5 - 72
⇒ y = -5 - 72
⇒ y = (-77) / (-7) = 11
∴ Required fraction = 9/11
- The ratio of incomes of two persons is 8 : 5 and the ratio of their expenditure i 2 : 1. If each of them manages to save ₹ 1000 per month, find the difference of their monthly income
-
View Hint View Answer Discuss in Forum
Let the incomes of two persons be 8x and 5x and their expenditure be 2y and y , respectively.
? Saving = Income - Expenditure
? 1000 = 8x - 2y ...(i) and
1000 = 5x - y ...(ii)Correct Option: B
Let the incomes of two persons be 8x and 5x and their expenditure be 2y and y , respectively.
∵ Saving = Income - Expenditure
∴ 1000 = 8x - 2y ...(i)
and 1000 = 5x - y ...(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. . (i) , we get
8x - 2y = 1000
10x - 2y = 2000
----------------------
-2x = -1000
∴ x = 500
∴ Monthly incomes are
8x = ₹ 4000 and
5x = ₹ 2500
∴ Difference = ₹ 4000 - 2500 = ₹ 1500
