8th Maths 2.4

Chapter 2

Linear Equations in One Variable

NCERT Class 8th solution of Exercise 2.1

NCERT Class 8th solution of Exercise 2.2

NCERT Class 8th solution of Exercise 2.3

NCERT Class 8th solution of Exercise 2.5

NCERT Class 8th solution of Exercise 2.6

Exercise 2.4

Q1. 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?
`text{Sol.}`
`text{Let Amina thinks of a number is x}`
`text{According to question}`
`(text{x} - 5/2)times8 = 3 times text{x}`
`text{8x - 20 = 3x}`
`text{8x - 3x = 20}`
`text{5x = 20}`
`text{x} = 20/5`
`text{x} = 4`
`text{Answer:}`
`text{The number is 4.}`


Q2. 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?
`text{Sol.}`
`text{Let a positive no. is x}`
`text{and another no. is 5x}`
`text{According to question}`
`text{2(x +21) = 5x + 21}`
`text{2x + 42 = 5x + 21}`
`text{5x - 2x = 42 - 21}`
`text{3x = 21}`
`text{x} = 21/3`
`text{x} = 7`
`text{5x} = 7times5 = 35`
`text{Answer:}`
`text{The numbers are 7 and 35.}`
Q3. Sum of the digits of a two-digit 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?
`text{Sol.}`
`text{Let tens digit is x}`
`text{and ones digit is 9 - x}`
`text{original number 10x + (9 - x)}`____`text{(A)`
`text{According to question}`
`text{[10(9 - x) + x ]+ 27 = 10x + (9 - x)}`
`text{90 - 10x + x + 27 = 10x + 9 - x}`
`text{63 - 9x = 9x + 9}`
`text{9x + 9x = 63 - 9}`
`text{18x = 54}`
`text{x} = 54/18`
`text{x} = 3`
`text{9 - x} = 9 - 3 = 6`
`text{Put these values in equation (A)}`
`text{10(3) + 6 = 36}`
`text{Answer:}`
`text{The two digit no. is 36.}`
Q4. 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?
`text{Sol.}`
`text{Let tens digit x}`
`text{and ones digit 3x}`
`text{original number 10x + 3x}`_______`text{(A)}`
`text{According to question}`
`text{(10x + 3x) + [10(3x) + x] = 88}`
`text{13x + 31x = 88}`
`text{44x = 88}`
`text{x} = 88/44`
`text{x} = 2`
`text{3x} = 3times2 = 6`
`text{Put these values in equation (A)}`
`text{10(2) + 6 = 26}`
`text{or}`
`62`
`text{Answer:}`
`text{The original no. is 26 or 62.}`
Q5. 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 ages?
`text{Sol.}`
`text{Let Shobo's present age x years}`
`text{and mother's present age 6x years}`
`text{After 5 years}`
`text{Shobo's age x + 5 years}`
`text{According to question}`
`text{3(x + 5) = 6x}`
`text{3x + 15 = 6x}`
`text{6x - 3x = 15}`
`text{3x = 15}`
`text{x} = 15/3`
`text{x} = 5`
`text{6x} = 6 times 5 = 30`
`text{Answer:}`
`text{Shobo's age 5 years and}`
`text{mother's age 30 years.}`
Q6. 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 `₹ 75000` to fence the plot. What are the dimensions of the plot?
`text{Sol.}`
`text{Let Length of rectangular plot 11x}`
`text{and Breadth of rectangular plot 4x}`
`text{According to qiestion}`
`text{Preimeter of rectangular plot = 2(L + B)}`
`text{Total cost of fence}/text{Rate} = text{2(11x + 4x)}`
`75000/100 = text{ 2(15x)}`
`750 = text{ 30x}`
`text{x} = 750/30`
`text{x} = 25`
`text{11x} = 11 times 25 = 275`
`text{4x} = 4 times 25 = 100`
`text{Answer:}`
`text{Length 275 meters and Breadth 100 meters.}`
Q7. 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.
For every `3` meters of the shirt material, he buys `2` meters of the trouser material. He sells the materials at `12`% and `10`% profit respectively. His total sale is `₹36600`. How much trouser material did he buy?
`text{Sol.}`
`text{Ratio of shirt and trouser material bought is 3 : 2}`
`text{Let the shirt material bought 3x}`
`text{and the trouser material bought 2x}`
`text{cost price of shirt material 3x}times 50 = 150text{x}`
`text{cost price of trouser material 2x}times 90 = 180text{x}`
`text{selling price of shirt material =} (text{cp}(100 + p))/100`

`text{sp} = (150text{x}(100 + 12))/100`

`text{sp} = (150text{x} times 112)/100`

`text{sp} = 168text{x}`
`text{selling price of trouser material =} (text{cp}(100 + p))/100`

`text{sp} = (180text{x}(100 + 10))/100`

`text{sp} = (180text{x} times 110)/100`

`text{sp} = 198text{x}`
`text{According to question}`
`text{Total sp = 168x + 198x}`
`text{36600 = 366x}`
`text{x} = 100`
`text{Length of trouser material 2}times 100 = 200text{ m}`
`text{Answer:}`
`text{Length of trouser material 200 m}`
Q8. 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.
`text{Sol.}`
`text{The no. of deer in the herd x}`
`text{and no. of deer are grazing } text{x}/2`
`text{and no. of deer are playing } 3/4times text{x}/2 = (3text{x})/8`
`text{According to question}`
`text{x - x}(1/2 + 3/8) = 9`
`text{x - x}((4 + 3)/8 )= 9`
`text{x - x} (7/8) = 9`
`text{8x - 7x}/8 = 9`
`text{x} = 9times8`
`text{x} =  72` 
`text{Answer:}`
`text{The no. of deer in the herd 72.}`
Q9. A grandfather is ten times older than his granddaughter. He is also `54` years older than her. Find their present ages.
`text{Sol.}`
`text{Let Granddaughter's present age x years}`
`text{and Grandfather's present age 10x years}`
`text{According to question}`
`text{10x - x = 54}`
`text{9x = 54}`
`text{x} = 54/9`
`text{x} = 6`
`text{10x} = 10 times 6 = 60`
`text{Answer:}`
`text{Granddaughter's present age 6 years and}`
`text{Grandfather's present age 60 years.}`
Q10. 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.
`text{Sol.}`
`text{Let son's age x years}`
`text{and Aman's age 3x years}`
`text{Before 10 years}`
`text{son's age (x - 10)}`
`text{and Aman's age (3x - 10)}` 
`text{According to question}`
`text{5(x - 10) = (3x - 10)}`
`text{5x - 50 = 3x - 10}`
`text{5x - 3x = 50 - 10}`
`text{2x = 40}`
`text{x} = 40/2`
`text{x} = 20`
`text{3x} = 3times20 = 60`
`text{Answer:}`
`text{Aman's age 60 years and}`
`text{son's age 20 years.}`

Comments

Post a Comment

Popular posts from this blog

MPBSE 10th & 12th Result

Image
MPBSE 10th & 12th Result मध्यप्रदेश माध्यमिक शिक्षा बोर्ड  [MPBSE ] भोपाल म.प्र. 10वीं और 12वीं का रिजल्ट प्राप्त करने के लिए आवश्यक दस्तावेज  कक्षा 10वीं और 12वीं का रिजल्ट प्राप्त करने के लिए आवश्यक दस्तावेज रोल नंबर, आवेदन क्रमांक  और अन्य सबमिट कर । 10वीं और 12वीं का रिजल्ट कहाँ से प्राप्त करें कक्षा  10वीं और  12वीं का रिजल्ट उम्मीदवार एमपीबीएसई की आधिकारिक वेबसाइट को टच करके  mpbse.mponline.gov.in 👈 या mpbse.nic.in 👈 या mpresults.nic.in 👈 या Jagranjosh.com 👈 या indianexpress.com 👈 या fastresult.in 👈 या hindustantimes.com 👈 या livehindustan.com 👈 या aajtak.in 👈 या indiatoday.in 👈 या amarujala.com 👈 या timesofindia.com 👈 या tv9hindi.com 👈 पर नतीजे देख सकते है । 10वीं और 12वीं के उम्मीदवारों को सलाह  यह परीक्षा जीवन का एक हिस्सा है, सारा जीवन नहीं । इस परीक्षा के परिणाम की कमियों से परेशान न होकर संयम और धैर्यपूर्वक स्वीकार करें । आपको आने वाले समय में इन कमियों को दूर करने का प्रयास करना होगा । जीवन में करने के लिए बहुत कुछ है ।  10वीं और 12वीं के बाद आगे क्या करें
Read more

10th Maths 4.3

Image
NCERT Class 10th solution of Exercise 4.1 NCERT Class 10th solution of Exercise 4.2 NCERT Class 10th solution of Exercise 4.4 NCERT Class 10th Maths Projects Like, share, and Subscribe. Exercise 4.3 Q1. Find the roots of the following quadratic equations, if they exist, by the method of completing the square : i) `2x^2-7x+3=0` ii) `2x^2+x-4=0` iii) `4x^2+4sqrt3x+3=0` iv) `2x^2+x+4=0` Sol. : i) `2x^2-7x+3=0` compare with `ax^2+bx+c=0` where `a=2, b=-7` and `c=3` `=b^2-4ac` `=(-7)^2-4(2)(3)` `=49-24` `=25>0` The roots exist. By completing the square `2x^2-7x+3=0` `x^2-(7x)/2+3/2=0` `x^2-(7x)/2=-3/2`   [Add `(7/4)^2` both sides] `x^2-(7x)/2+(7/4)^2=-3/2+(7/4)^2`  `x^2-(2(7x))/(2(2))+(7/4)^2=-3/2+49/16` `(x-7/4)^2=(-24+49)/16` `(x-7/4)^2=25/16` `(x-7/4)^2=(5/4)^2` `(x-7/4)^2-(5/4)^2=0` [`a^2-b^2=(a+b)(a-b)`] `(x-7/4-5/4)(x-7/4+5/4)=0` `(x-12/4)(x-2/4)=0` `(x-3)(x-1/2)=0` `x-3=0` `x=3` `x-1/2=0` `x=1/2` Answer : `x=3, 1/2` ii) `2x^2+x-4=0` compare with `ax^2+bx+c=0` where `a=2, b=1` and
Read more

RSKMP 5th & 8th Result

Image
RSKMP 5th & 8th Result राज्य शिक्षा केंद्र  [RSKMP ] भोपाल म.प्र. 5वीं और 8वीं का रिजल्ट प्राप्त करने के लिए आवश्यक दस्तावेज  कक्षा 5वीं और 8वीं का रिजल्ट प्राप्त करने के लिए आवश्यक दस्तावेज रोल नंबर, आवेदन क्रमांक, समग्र आईडी और अन्य सबमिट कर । Like, Share, and Subscribe. 5वीं और 8वीं का रिजल्ट कहाँ से प्राप्त करें कक्षा  5वीं और  8वीं का रिजल्ट उम्मीदवार नीचे दी वेबसाइट को टच करके 5th और 8th का रिजल्ट  🫲 5th और 8th का रिजल्ट  🫲 5th और 8th का रिजल्ट  🫲 5th और 8th का रिजल्ट  🫲 पर नतीजे देख सकते है । 5वीं और 8वीं के उम्मीदवारों को सलाह  यह परीक्षा जीवन का एक हिस्सा है, सारा जीवन नहीं । इस परीक्षा के परिणाम की कमियों से परेशान न होकर संयम और धैर्यपूर्वक स्वीकार करें । आपको आने वाले समय में इन कमियों को दूर करने का प्रयास करना होगा । जीवन में करने के लिए बहुत कुछ है ।  ------x---- राज्य शिक्षा केंद्र  [RSKMP ] भोपाल म.प्र. 5वीं और 8वीं का रिजल्ट प्राप्त करने के लिए आवश्यक दस्तावेज  कक्षा 5वीं और 8वीं का रिजल्ट प्राप्त करने के लिए आवश्यक दस्तावेज रोल नंबर, आवेदन क्रमांक, और अन्य सब
Read more