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All questions of Linear Equations in One Variable for Class 8 Exam
Arun’s age is three times his son’s age. 10 years age he was 5 times his son’s age. What is the sum of their present ages?- a)60 years
- b)70 years
- c)80 years
- d)90 years
Correct answer is option 'C'. Can you explain this answer?
Arun’s age is three times his son’s age. 10 years age he was 5 times his son’s age. What is the sum of their present ages?
a)
60 years
b)
70 years
c)
80 years
d)
90 years
 | Geetika Shah answered |
Let Son’s age = x years
∴ Arun’s age = 3x.
Now 10 years ago, son’s age = x – 10.
Given Arun’s age = 3x – 10
⇒ 3x -10 = 5 (x – 10)
⇒ 3x – 10 = 5x – 50
2x = 40 ⇒ x = 20 years
Arun’s age = 3 × 20 = 60 years
Sum of Arun’s and Son’s age = 20 + 60
= 80 years
∴ Arun’s age = 3x.
Now 10 years ago, son’s age = x – 10.
Given Arun’s age = 3x – 10
⇒ 3x -10 = 5 (x – 10)
⇒ 3x – 10 = 5x – 50
2x = 40 ⇒ x = 20 years
Arun’s age = 3 × 20 = 60 years
Sum of Arun’s and Son’s age = 20 + 60
= 80 years
Nirmal thinks of a number and subtracts 5/2 from it. He multiplies the result by 8. The result now obtained is 3 times the same number he thought of. Find the number.
a)4b)5c)6d)8Correct answer is option 'A'. Can you explain this answer?
 | Ananya Das answered |
Let the number be x.
⇒ 8x - 20 = 3x
⇒ 5x = 20
⇒ x = 4
⇒ 8x - 20 = 3x
⇒ 5x = 20
⇒ x = 4
The difference between the digits of a two-digit number is 3. If the digits are interchanged and the resulting number is added to the original number we get 143. What was the original number?- a)58
- b)85 9
- c)78
- d)87
Correct answer is option 'A'. Can you explain this answer?
The difference between the digits of a two-digit number is 3. If the digits are interchanged and the resulting number is added to the original number we get 143. What was the original number?
a)
58
b)
85 9
c)
78
d)
87
| | Geetika Shah answered |
Let the unit’s digit be x.
Ten’s digit = x + 3.Original number =10(x + 3) + 1(x)
= 10x + 30 + x
= 11x + 30
After interchange, resulting number
= 10 (x) + 1 (x + 3)
= 10x + x + 3
= 11x + 3
∴ 11x + 3 + 11x + 30 = 143
⇒ 22x + 33 = 143
⇒ 22x = 143 – 33
⇒ 22x = 110
⇒
Original number = 11x + 3 = 11 × 5 + 3
= 55 + 3 = 58
Ten’s digit = x + 3.Original number =10(x + 3) + 1(x)
= 10x + 30 + x
= 11x + 30
After interchange, resulting number
= 10 (x) + 1 (x + 3)
= 10x + x + 3
= 11x + 3
∴ 11x + 3 + 11x + 30 = 143
⇒ 22x + 33 = 143
⇒ 22x = 143 – 33
⇒ 22x = 110
⇒
Original number = 11x + 3 = 11 × 5 + 3
= 55 + 3 = 58
The sum of the digits of a two number is 9. If 9 is subtracted from the number its digits are interchanged. What is the number?- a)54
- b)63
- c)72
- d)45
Correct answer is option 'A'. Can you explain this answer?
The sum of the digits of a two number is 9. If 9 is subtracted from the number its digits are interchanged. What is the number?
a)
54
b)
63
c)
72
d)
45
 | Shubham Sharma answered |
Let the unit’s digit be x.
Ten’s digit = 9 – x
Number = 10 (9 – x) + 1(x)
= 90 – 10x + x= 90 – 9x
90 – 9x – 9 = x(10) + 1(9 – x)
⇒ 81 – 9x = 10x + 9 – x
⇒ 81 – 9x = 9x + 9
⇒ 18x = 72 ⇒ x = 4
Number = 90 – 9 × 4 = 90 – 36 = 54
Ten’s digit = 9 – x
Number = 10 (9 – x) + 1(x)
= 90 – 10x + x= 90 – 9x
90 – 9x – 9 = x(10) + 1(9 – x)
⇒ 81 – 9x = 10x + 9 – x
⇒ 81 – 9x = 9x + 9
⇒ 18x = 72 ⇒ x = 4
Number = 90 – 9 × 4 = 90 – 36 = 54
The sum of three consecutive multiples of 11 is 363. Which of these multiple is greatest?- a)121
- b)131
- c)132
- d)122
Correct answer is option 'C'. Can you explain this answer?
The sum of three consecutive multiples of 11 is 363. Which of these multiple is greatest?
a)
121
b)
131
c)
132
d)
122
| | Ananya Das answered |
Let the numbers be
11x, 11(x + 1), 11(x + 2)
Hence 11x + 11(x + 1) + 11(x + 2) = 363
⇒ 11x + 11x + 11 + 11x + 22 = 363
⇒ 33x + 33 = 363
⇒
Greatest multiple = 11(x + 2)
= 11 (10 + 2) = 11 × 12 = 132
11x, 11(x + 1), 11(x + 2)
Hence 11x + 11(x + 1) + 11(x + 2) = 363
⇒ 11x + 11x + 11 + 11x + 22 = 363
⇒ 33x + 33 = 363
⇒
Greatest multiple = 11(x + 2)
= 11 (10 + 2) = 11 × 12 = 132
A field can be ploughed in 18 days. If everyday an additional area of 16 hectares is ploughed, the field can be ploughed in 12 days. What is the area of the field?- a)512 hectares
- b)576 hectares
- c)528 hectares
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
A field can be ploughed in 18 days. If everyday an additional area of 16 hectares is ploughed, the field can be ploughed in 12 days. What is the area of the field?
a)
512 hectares
b)
576 hectares
c)
528 hectares
d)
None of these
| | Shubham Sharma answered |
Let the area of the field ploughed daily be x hectares.
Area of the field = 18x
⇒ 18x = (x + 16) 12
⇒ 18x = 12x + 16 × 12
⇒ 6x = 16 × 12
⇒
Area of the field = 18 × 32 = 576 hectares
Area of the field = 18x
⇒ 18x = (x + 16) 12
⇒ 18x = 12x + 16 × 12
⇒ 6x = 16 × 12
⇒
Area of the field = 18 × 32 = 576 hectares
A grand father is ten times older than his grandson. He is then also 54 years older than him. What is the difference of their present ages?- a)54 yeas
- b)45 years
- c)50 years
- d)52 years
Correct answer is option 'A'. Can you explain this answer?
A grand father is ten times older than his grandson. He is then also 54 years older than him. What is the difference of their present ages?
a)
54 yeas
b)
45 years
c)
50 years
d)
52 years
| | Ananya Das answered |
Let the age of grand son be x years.
Grand father’s age = 10x.
⇒ 10x = 54 + x
⇒ 9x = 54
⇒ x = 6
Grand father’s age = 10 × 6 = 60 years
Difference of their present ages = 60 – 6 = 54.
Grand father’s age = 10x.
⇒ 10x = 54 + x
⇒ 9x = 54
⇒ x = 6
Grand father’s age = 10 × 6 = 60 years
Difference of their present ages = 60 – 6 = 54.
The ages of Raju and Rajan are in the ratio 5 : 8. If Raju was 5 years older and Rajan 4 years younger, the age of Raju would have been the same as the age of Rajan. What is the age of Raju?- a)15 years
- b)16 years
- c)24 years
- d)13 years
Correct answer is option 'A'. Can you explain this answer?
The ages of Raju and Rajan are in the ratio 5 : 8. If Raju was 5 years older and Rajan 4 years younger, the age of Raju would have been the same as the age of Rajan. What is the age of Raju?
a)
15 years
b)
16 years
c)
24 years
d)
13 years
 | Kavya Saxena answered |
Let Raju’s age = 5x.
∴ Rajan ‘s age = 8x
∴ 5x + 5 = 8x – 4
⇒ 3x = 9 ⇒ x = 3
Raju’s age = 5 × = 15 years
∴ Rajan ‘s age = 8x
∴ 5x + 5 = 8x – 4
⇒ 3x = 9 ⇒ x = 3
Raju’s age = 5 × = 15 years
What is the value of x in the given equatiom?
- a)x = 1
- b)x = - 1
- c)x = 2
- d)x = - 2
Correct answer is option 'A'. Can you explain this answer?
What is the value of x in the given equatiom?
a)
x = 1
b)
x = - 1
c)
x = 2
d)
x = - 2
| | Amit Kumar answered |
⇒ 5x + 30 – 30 + 15x = 30x – 10
⇒ 20x + 10 = 30x
⇒ 10x = 10 ⇒ x = 1
A shirt is sold for Rs. 1498 and the seller gains 7% on it. What is the cost price of the shirt ?- a)1600
- b)1500
- c)1400
- d)1450
Correct answer is option 'C'. Can you explain this answer?
A shirt is sold for Rs. 1498 and the seller gains 7% on it. What is the cost price of the shirt ?
a)
1600
b)
1500
c)
1400
d)
1450
| | Amit Kumar answered |
Let the cost price of the shirt be Rs. x.
∴ x + 7% of x = 1498
⇒
⇒ 107x 1498 x 100
⇒
∴ x + 7% of x = 1498
⇒
⇒ 107x 1498 x 100
⇒
What is the value of x if
- a)m
- b)n
- c)-m
- d)- n
Correct answer is option 'C'. Can you explain this answer?
What is the value of x if
a)
m
b)
n
c)
-m
d)
- n
| | Shubham Sharma answered |
⇒ (x – n) (m – n) = (x + n)(m + n)
⇒ mx – mn – nx + n2 = mx + mn + nx + n2
⇒ - mn – nx = mn + nx
⇒ 2nx = -2mn
⇒
⇒ mx – mn – nx + n2 = mx + mn + nx + n2
⇒ - mn – nx = mn + nx
⇒ 2nx = -2mn
⇒
The sum of two numbers is 360. If 65% of one number is equal to 85% of the other. What is the largest number among them?- a)204
- b)156
- c)256
- d)214
Correct answer is option 'A'. Can you explain this answer?
The sum of two numbers is 360. If 65% of one number is equal to 85% of the other. What is the largest number among them?
a)
204
b)
156
c)
256
d)
214
 | Arshiya Tiwari answered |
Let the one number be x.
Other number = 360 – x
Now 65% of x = 85% of (360 – x)
⇒ 65 x + 85x = 85 × 360
⇒ 150x = 85 × 360
⇒
Other number = 360 – x
Now 65% of x = 85% of (360 – x)
⇒ 65 x + 85x = 85 × 360
⇒ 150x = 85 × 360
⇒
What is the value of x in the given equation
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'D'. Can you explain this answer?
What is the value of x in the given equation
a)
2
b)
3
c)
4
d)
5
| | Geetika Shah answered |
⇒ 53x - 41 = 38x + 34
⇒ 15x = 34 + 41
⇒
Mohaesh travelled 1/2 th of his Journey by bus, 1/4 th by taxi, 3/5 th by train and remaining 8 km by foot. What is the length of his total Journey?- a)120 km
- b)240 km
- c)220 km
- d)320 km
Correct answer is option 'D'. Can you explain this answer?
Mohaesh travelled 1/2 th of his Journey by bus, 1/4 th by taxi, 3/5 th by train and remaining 8 km by foot. What is the length of his total Journey?
a)
120 km
b)
240 km
c)
220 km
d)
320 km
 | Vani Patel answered |
Let length of total Journey be x km.
⇒ 39x + 320 = 40x
⇒ x = 320
⇒ 39x + 320 = 40x
⇒ x = 320
A certain number of workers can finish a piece of work in 70 days. If there are 20 men less, it would take 10 days more for the same work to be finished. How many workers were there in starting?- a)150
- b)160
- c)140
- d)152
Correct answer is option 'B'. Can you explain this answer?
A certain number of workers can finish a piece of work in 70 days. If there are 20 men less, it would take 10 days more for the same work to be finished. How many workers were there in starting?
a)
150
b)
160
c)
140
d)
152
| | Punya Chakraborty answered |
Let the no. of workers in starting be x.
∴ 70 × x = (x – 20) 80
⇒ 70 x = 80x – 20 × 80
⇒ 10x = 20 × 80
⇒
∴ 70 × x = (x – 20) 80
⇒ 70 x = 80x – 20 × 80
⇒ 10x = 20 × 80
⇒
A boat goes downstream and covers the distance between two ports in 4 hours, while it covers the same distance upstream in 5 hours. If the speed of the stream is 2km/hour. what is the speed of boat in still water ?- a)18 km/hour
- b)16 km/hour
- c)20 km/hour
- d) 15 km/hour
Correct answer is option 'A'. Can you explain this answer?
A boat goes downstream and covers the distance between two ports in 4 hours, while it covers the same distance upstream in 5 hours. If the speed of the stream is 2km/hour. what is the speed of boat in still water ?
a)
18 km/hour
b)
16 km/hour
c)
20 km/hour
d)
15 km/hour
| | Srestha Desai answered |
Let the speed of boat in still water be x km/hour.
∴ (x + 2) 4 = (x – 2) 5
⇒ 4x + 8 = 5x - 10
⇒ x = 18 km/hr
∴ (x + 2) 4 = (x – 2) 5
⇒ 4x + 8 = 5x - 10
⇒ x = 18 km/hr
Half of a herd of deer are grazing in the field and three fourth of remaining are playing nearby. The rest nine are drinking water from the river. What is the number of deer in the herd?- a)72
- b)62
- c)74
- d)80
Correct answer is option 'A'. Can you explain this answer?
Half of a herd of deer are grazing in the field and three fourth of remaining are playing nearby. The rest nine are drinking water from the river. What is the number of deer in the herd?
a)
72
b)
62
c)
74
d)
80
 | Tanvi Chauhan answered |
Let number of deer be x.
∴
⇒
⇒ 4x + 3x 72 = 8x
⇒ x = 72
∴
⇒
⇒ 4x + 3x 72 = 8x
⇒ x = 72
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