Class 8 - Mathematics
Linear Equations in One Variable - Exercise 2.4
Top Block 1
Question: 1. Amina thinks of a number and subtracts 5⁄2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?
Answer :
Let Amina think a number 𝓍
Question: 2. A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?
Answer :
Let another number be 𝓍
Then positive number = 5𝓍
According to the question,
⇒ 5𝓍 + 21 = 2𝓍 + 42
⇒ 5𝓍 – 2𝓍 = 42 – 21
⇒ 3𝓍 = 21
⇒ 𝓍 = 7
Hence another number = 7 and positive number = 7 x 5 = 35
Question: 3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
Answer :
Let the unit place digit of a two-digit number be 𝓍
Therefore, the tens place digit = 9 – 𝓍
∵ 2-digit number = 10 x tens place digit + unit place digit
∴ Original number = 10(9 – 𝓍) + 𝓍
According to the question, New number
= Original number + 27
⇒ 10𝓍 + (9 – 𝓍) = 10(9 – 𝓍) + 𝓍 + 27
⇒ 10 + 9 – 𝓍 =90 – 10𝓍 + 𝓍 + 27
⇒ 9𝓍 + 9 = 117 – 9𝓍
⇒ 9𝓍 + 9𝓍 = 117 – 9
⇒ 18𝓍 = 108
⇒ 𝓍 = 6
Hence, the 2-digit number
⇒ = 10(9 – 𝓍) + 𝓍
⇒ = 10(9 – 6) + 6
⇒ = 10 x 3 + 6
⇒ = 30 + 6
⇒ = 36
Question: 4. One of the two digits of a two-digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
Answer :
Let the unit place digit of a two-digit number be 𝓍.
Therefore, the tens place digit = 3𝓍
∵ 2-digit number = 10 x tens place digit + unit place digit
∴ Original number = 10 x 3𝓍 + 𝓍 = 30𝓍 + 𝓍 = 31𝓍
According to the question, New number + Original number = 88
⇒ 10𝓍 + 3𝓍 + 31𝓍 = 88
⇒ 44𝓍 = 88
⇒ 𝓍 = 2
Hence, the 2-digit number = 31𝓍 = 31 x 2 = 62
Question: 5. Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present age?
Answer :
Let Shobo’s present age be 𝓍 years.
And Shobo’s mother’s present age = 6𝓍 years
According to the question,
⇒ 𝓍 + 5 = 1⁄3 x 6𝓍
⇒ 𝓍 + 5 = 2𝓍
⇒ 2𝓍 = 𝓍 + 5
⇒ 2𝓍 – 𝓍 = 5
⇒ 𝓍 = 5
Hence, Shobo’s present age = 5 years
And Shobos’s mother’s age = 6 x 5 = 30 years.
Question: 6. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11 : 4. At the rate `100 per meter it will cost the village panchayat`75,000 to fence the plot. What are the dimensions of the plot?
Answer :
Let the length and breadth of the rectangular plot be 11𝓍 and 4𝓍 respectively.
Mddle block 1
Question: 7. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him `50 per meter and trouser material that costs him `90 per meter.
Answer :
Let ratio between shirt material and trouser material be 3𝓍 : 2𝓍
Question: 8. Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.
Answer :
Let the total number of deer in the herd be 𝓍.
Question: 9. A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.
Answer :
Let present age of granddaughter be 𝓍 years.
Therefore, Grandfather’s age = 10𝓍 years
According to question,
10𝓍 = 𝓍 + 54
⇒ 10𝓍 – 𝓍 = 54
⇒ 9𝓍 = 54
⇒ 𝓍 = 6 years
Hence, Granddaughter’s age = 6 years and grandfathers’s age = 10 x 6 = 60 years.
Question: 10. Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.
Answer :
Let the present age of Amon’s son be 𝓍 years.
Therefore, Aman’s age = 3𝓍 years
According to question,
3𝓍 – 10 = 5(𝓍- 10)
⇒ 3𝓍 – 10 = 5𝓍 – 50
⇒ 3𝓍 – 5𝓍 = – 50 + 10
⇒ – 2𝓍 = – 40
⇒ 𝓍 = 20
Hence, Aman’s son’s age = 20 years
And Aman’s age = 3 x 2 = 60 years.