3 Mark Question - Maths STD 8 Questions - Vidyadip

Questions

3 Mark Question

Take a timed test

15 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks

I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes that I have is ten more than the number of five rupee notes, how many notes do I have in each denomination?

Answer

Total amount = Rs. 1000
Let the number of five rupee note = x
$\therefore$ Ten rupees notes = x + 10
According to the condition,
(x + 10) × 10 + 5x × x = 1000
⇒ 10a + 100 + 5a = 1000
⇒ 15a = 1000 - 100 = 900
$\Rightarrow\text{x}=\frac{900}{15}=60$
$\therefore$ Numbe of five rupees notes = 60
and number of ten rupees notes = 60 + 10 = 70

View full question & answer→

Question 23 Marks

Solve the following equation and also check your result in case:
$\frac{7\text{y}+2}{5}=\frac{6\text{y}-5}{11}$

Answer

$\frac{7\text{y}+2}{5}=\frac{6\text{y}-5}{11}$
$77\text{y}-22=30\text{y}-25$
$77\text{y}-30\text{y}=-25-22$
$47\text{y}=-47$
$\text{y}=\frac{-47}{47}=-1$
Verification:
$\text{L.H.S.}=\frac{-7+2}{5}=\frac{-5}{5}=-1$
$\text{R.H.S.}=\frac{-6-5}{11}=\frac{-11}{11}=-1$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for y}=-1$

View full question & answer→

Question 33 Marks

Solve the following equation and also check your result in case:
$\frac{3\text{x}}{4}-\frac{(\text{x}-1)}{2}=\frac{(\text{x}-2)}{3}$

Answer

$\frac{3\text{x}}{4}-\frac{(\text{x}-1)}{2}=\frac{(\text{x}-2)}{3}$
$\frac{3\text{x}-2\text{x}{+2}}{4}=\frac{\text{x}-2}{3}$
$4\text{x}-8=3\text{x}+6$
$\text{x}=14$
Check:
$\text{L.H.S.}=\frac{3\times14}{4}-\frac{14-1}{2}=\frac{21}{2}-\frac{13}{2}=\frac{8}{2}=4$
$\text{R.H.S.}=\frac{14-2}{3}=\frac{12}{3}=4$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for x}=14$

View full question & answer→

Question 43 Marks

Four-fifth of a number is more than three-fourth of the number by 4. Find the number.

Answer

Let the requierd number = x
Then Four-fifth of the number $=\frac{4}{5}\text{x}$
And tree - fourth $=\frac{3}{4}\text{x}$
$\therefore \frac{4}{5}\text{x}-\frac{3}{47}\text{x}=4$
$\Rightarrow\frac{16\text{x}-15\text{x}=8}{20}$ (L.C.M.of 5, 4 = 20)
$\therefore$ Required number = 80
Chake : $\frac{4}{5}$ of 80 $-\frac{3}{4}$ of 80
= 64 - 60 = 4 wich is given
$\therefore$ Our answer is correct.

View full question & answer→

Question 53 Marks

Solve the following equation and also check your result in case:
$\text{x}-\frac{(\text{x}-1)}{2}=1-\frac{(\text{x}-2)}{3}$

Answer

$\text{x}-\frac{(\text{x}-1)}{2}=1-\frac{(\text{x}-2)}{3}$
$\frac{2\text{x}-\text{x+1}}{2}=\frac{3-\text{x}+2}{3}$
$\frac{\text{x}+1}{2}=\frac{5-\text{x}}{3}$
$3\text{x}+3=10-2\text{x}$
$5\text{x}=10-3$
$\text{x}=\frac{7}{5}$
Check:
$\text{L.H.S.}=\frac{7}{5}-\frac{\frac{7}{5}-1}{2}=\frac{7}{5}-\frac{1}{5}=\frac{6}{5}$
$\text{R.H.S.}=1-\frac{\frac{7}{5}-2}{3}=1-\frac{-3}{15}=\frac{6}{5}$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for x}=\frac{7}{5}$

View full question & answer→

Question 63 Marks

There are 180 multiple choice questions in a test. If a candidate gets 4 marks for every correct answer and for every unattempted or wrongly answered question one mark is deducted from the total score of correct answers. If a candidate scored 450 marks in the test, how many questions did he answer correctly?

Answer

Number of total quations = 180
Let the candidate answers questions correctly = x
$\therefore$ Uncorrect or unttended quastions = 180 - x
Total score he got = 450
According to the condition
x × 4-(180 - x) × 1 = 450
⇒ 4x - 180 + x - = 450
⇒ 5x = 450 + 180 = 630
$\Rightarrow\text{x}=\frac{630}{5}=126$
Number of question which answered correctly = 126

View full question & answer→

Question 73 Marks

Find a positive value of x for which the given equation is satisfied.
$\frac{\text{y}^2+4}{3\text{y}^2+7}=\frac{1}{2}$

Answer

$\frac{\text{y}^2+4}{3\text{y}^2+7}=\frac{1}{2}$By cross multiplication:
$2(\text{y}^2+4)=3\text{y}^2+7$
$\Rightarrow2\text{y}^2+8=3\text{y}^2+7$
$\Rightarrow3\text{y}^2-2\text{y}^2=8-7$
$\Rightarrow\text{y}^2=1$
$\therefore\text{y}=\underline{+}\sqrt{1}=\underline{+}1$
$\because $ we have to take only positive value of x
$\therefore\text{y}=1$

View full question & answer→

Question 83 Marks

Solve the following equation and verify your answer:
$\frac{2\text{y}+5}{\text{y}+4}=1$

Answer

$\frac{2\text{y}+5}{\text{y}+4}=1$By cross multiplication:
$2\text{y}+5=\text{y}+4$ $\Rightarrow2\text{y}-\text{y}=4-5$ (By transposition) $\Rightarrow\text{y}=-1$ $\therefore\text{y}=-1$Verification:
$\text{L.H.S.}=\frac{2\text{y}+5}{\text{y}+4}=\frac{2(-1)+5}{-1+4}=\frac{-2+5}{-1+4}$ $=\frac{3}{3}=1=\text{R.H.S.}$

View full question & answer→

Question 93 Marks

In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to each, the numerator and the denominator, the new fraction is $\frac{2}{3}.$ Find the original number.

Answer

Let numerator = x
Then denominator = 2x - 2
Fraction $=\frac{\text{x}}{2\text{x}-2}$
According to the condition:
$\frac{\text{x}+3}{2\text{x}-2+3}=\frac{2}{3}$
$\Rightarrow\frac{\text{x}+3}{2\text{x}+1}=\frac{2}{3}$
By cross multiplication
3(x + 3) = 2(2x + 1)
⇒ 3x + 9 = 4x + 2
⇒ 9 - 2 = 4x - 3x
⇒ x = 7
$\therefore$ Number $=\frac{\text{x}}{2\text{x}-2}$
$=\frac{7}{2\times7-2}$
$=\frac{7}{14-2}$
$=\frac{7}{12}$

View full question & answer→

Question 103 Marks

A steamer goes downstream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1km/ hr, find the speed of the steamer in still water and the distance between the ports.

Answer

Time taken by a steamer downstream = 9 hours
and upstream = 10 hours speed of steamer = 1km/ hr.
Let speed of the condition:
9(x + 1) = 10(x - 1)
9x + 9 = 10x - 10
⇒ 10x - 9x
= 9 + 10
⇒ x = 19
$\therefore $ Speed of the steamer in still water = 19 km/ h
and distance between two ports = 9(a + 1) = 9(19 + 1) = 9 × 20 = 180km.

View full question & answer→

Question 113 Marks

Find a positive value of x for which the given equation is satisfied.
$\frac{\text{x}^2-9}{5+\text{x}^2}=\frac{-5}{9}$

Answer

$\frac{\text{x}^2-9}{5+\text{x}^2}=\frac{-5}{9}$By cross multiplication:
$9(\text{x}^2-9)=-5(5+\text{x}^2)$
$\Rightarrow9\text{x}^2-81=-25-5\text{x}^2$
$\Rightarrow9\text{x}^2+5\text{x}^2=-25+81$
$\Rightarrow14\text{x}^2=56$
$\Rightarrow\text{x}^2=\frac{56}{14}=4$
$\therefore\text{x}=\underline{+}\sqrt{4}=\underline{+}2$
$\because $ we have to take only positive value of x
$\therefore\text{x}=2$

View full question & answer→

Question 123 Marks

The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and the numerator by 2, we get the rational number $\frac{1}{2}.$ Find the rational number.

Answer

Let denominator of the given rational number = x
Then numerator = x - 3
$\therefore$ Rational number $=\frac{\text{x}-3}{\text{x}}$
According to the condition:
$\frac{\text{x}-3+2}{\text{x}+5}=\frac{1}{2}$
$\Rightarrow\frac{\text{x}-1}{\text{x}+5}=\frac{1}{2}$
By cross multiolication
2(x - 1) = x + 5
⇒ 2x - 2 = x + 5
⇒ 2x - x = 5 + 2
⇒ x = 7
$\therefore$ Rational number $=\frac{\text{x}-3}{\text{x}}=\frac{7-3}{7}=\frac{4}{7}$

View full question & answer→

Question 133 Marks

Solve the following equation and also check your result in case:
$\frac{\text{a}-8}{3}=\frac{\text{a}-3}{2}$

Answer

$\frac{\text{a}-8}{3}=\frac{\text{a}-3}{2}$
$2\text{a}-16=3\text{a}-9$
$3\text{a}-2\text{a}=-16+9$
$\text{a}=-7$
Verification:
$\text{L.H.S.}=\frac{-7-8}{3}=\frac{-15}{3}=-5$
$\text{R.H.S.}=\frac{-7-3}{2}=\frac{-10}{2}=-5$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for a}=-7$

View full question & answer→

Question 143 Marks

Solve the following equation and verify your answer:
$\frac{5\text{x}-7}{3\text{x}}=2$

Answer

$\frac{5\text{x}-7}{3\text{x}}=\frac{2}{1}$By cross multiplication:
$2\times3\text{x}=5\text{x}-7$ $\Rightarrow6\text{x}-5\text{x}=-7$ $\Rightarrow\text{x}=-7$ (By transposition) $\therefore\text{x}=-7$Verification:
$\text{L.H.S.}=\frac{5\text{x}-7}{3\text{x}}=\frac{5\times(-7)-7}{3(-7)}$ $=\frac{-35-7}{-21}=\frac{-42}{-21}=\frac{2}{1}=\text{R.H.S.}$

View full question & answer→

Question 153 Marks

Solve the following equation and also check your result in case:
$\frac{2\text{x}+5}{3}=3\text{x}-10$

Answer

$\frac{2\text{x}+5}{3}=3\text{x}-10$
$2\text{x}+5=9\text{x}-30$
$9\text{x}-2\text{x}=5+30$
$7\text{x}=35$
$\text{x}=\frac{35}{7}$
$\text{x}=5$
Verification:
$\text{L.H.S.}=\frac{10+5}{3}=\frac{15}{3}=5$
$\text{R.H.S.}=15-10=5$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for x}=5$

View full question & answer→

Generate Paper Free All Linear Equations in One Variable topics