Exercise 1.6
Q1 | Ex-1.6 | Class 8 | ML Aggarwal | Rational Numbers | Chapter 1 | myhelper
OPEN IN YOUTUBE
Question 1
In a bag, there are 20 kg of fruits. If $7\frac{1}{6}$ kg of these fruits be oranges and $8\frac{2}{3}$ kg of three are apples and rest are grapes. Find the mass of the grapes in the bag.
Sol :
$\begin{aligned} \text { Total fruits } &=20 \mathrm{~kg} \\ \text { oranges } &=7 \frac{1}{6} \mathrm{~kg} \\ \text { Apples } &=8 \frac{2}{3} \mathrm{~kg} \end{aligned}$
let grapes =x
$7 \frac{1}{6}+8 \frac{2}{3}+x=20$
$\frac{43}{6}+\frac{26}{3}+x=20$
$\frac{(43 \times 1)+(26 \times 2)}{6}+x=20$
$\frac{43+52}{6}+x=20$
$\begin{aligned} \frac{95}{6}+x &=20 \\ x &=\frac{20}{1}-\frac{95}{6} \\ x &=\frac{120-95}{6} \\ x &=\frac{25}{6} \mathrm{~kg} \end{aligned}$
$\therefore$ Beg contain $4 \frac{1}{6}$ kg of grapes.
Question 2
The population of a city is 6,63,432. If $\frac{1}{2}$ of the population are adult males and $\frac{1}{3}$ of the population are adult females, then find the number of children in the city.
Sol :
Total population of city =6,63,432
Adult male $=\frac{1}{2}$ of total population
Adult females $2 \frac{1}{3}$ of total population
Adult male + Adult female terms + children = Total city
$\frac{1}{2}(6,63,432)+\frac{1}{3}(663432)+$ Children $=6163432$
$\frac{5}{6}(663432)+$ children $=663432$
children $=663432\left(1-\frac{5}{6}\right)$
$=663432 \times \frac{1}{6}$
Children =110572
no. of children in city $=110,572$
Question 3
In an election of housing society, there are 30 voters. Each of them gives the vote. Three persons X, Y and Z are standing for the post of Secretary. If Mr X got $\frac{2}{5}$ of the total votes and Mr Z got $\frac{1}{3}$ of the total votes, then find the number of votes which Mr Y got.
Sol :
Total votes =30
No. of votes for Mr. $x=\frac{2}{5}$ of $30=\frac{2}{5}(30)$
No. of votes for $M r \cdot z=\frac{1}{3} (30)$
Let Mr.Y votes =x
=$\therefore \quad \frac{2}{5}(30)+x+\frac{1}{3}(30)=30$
=12+x+10=30
=x+22=30
=x=30-22
x=8
No. of votes for Mr. y = 8
Question 4
A person earns ₹ 100 in a day. If he spent ₹ $14 \frac{2}{7}$ on food and $30\frac{2}{3}$ on petrol. How much did he save on that day?
Sol :
Total earnings =₹ 100
Rupees spent on food $=₹ 14 \frac{2}{7}$
Rupees spent on petrol $=₹ 30 \frac{2}{3}$
Let Savings on that day =x
$14 \frac{2}{7}+30 \frac{2}{3}+x=100$
$\frac{100}{7}+\frac{92}{3}+x=100$
$\begin{aligned}\left(\frac{100 \times 3)+(92 \times 7)}{21}\right.&+x=100 \\ x &=100-\frac{944}{21} \end{aligned}$
$x=\frac{1156}{21}=55 \frac{1}{21}$
$\therefore$ savings $=₹ 55 \frac{1}{21}$
Question 5
In an examination, 400 students appeared. If $\frac{2}{3}$ of the boys and all 130 girls passed in the examination, then find how many boys failed in an examination?
Sol :
Total students =400
no.of girls =130
no. of boys appeared for exam $=400-130$$=270$
no. of boys passed in exam $=\frac{2}{3}(270)$ $=180$
no. of boys failed in exam = Total boys - passed boys
=270-180
=90
$\therefore$ no. of boys failed in exam =90
Question 6
A car is moving at the speed of $40\frac{2}{3}$ km/h. Find how much distance will it cover in $\frac{9}{10}$ hours?
Sol :
speed of Car$ =40 \frac{2}{3} \mathrm{Km} / \mathrm{h}$
time $=\frac{9}{10} \mathrm{hr}$
distance traveled car = speed ｘtime
$=40 \frac{2}{3} \times \frac{9}{10}$
$=\frac{122}{3} \times \frac{9}{10}$
$=\frac{183}{5}$
$=36 \frac{3}{5} \mathrm{~km}$
Q7 | Ex-1.6 | Class 8 | ML Aggarwal | Rational Numbers | Chapter 1 | myhelper
OPEN IN YOUTUBE
Question 7
Find the area of a square lawn whose one side is $5\frac{7}{9}$ m long.
Sol :
Side of square = $5 \cdot \frac{7}{9} m$
$S=\frac{52}{9} m$
$\begin{aligned} \text { Area of square } &=S^{2} \\ &=\frac{52}{9} \times \frac{52}{9} \\ &=\frac{2704}{81} \\ \text { Area of square } &=33 \frac{31}{81} \mathrm{~m}^{2} \end{aligned}$
Question 8
Perimeter of a rectangle is $15\frac{3}{7}$ m. If the length is $4\frac{2}{7}$ m, find its breadth.
Sol :
Perimeter of rectangle = $15 \frac{3}{7} m$
length of rectangle (l) = $4 \frac{2}{7} m$
perimeter = 2 (l+b)
=$15 \frac{3}{7}=2\left(4 \frac{2}{7}+b\right)$
=$\frac{108}{7}=2\left(\frac{30}{7}+b\right)$
=$\frac{3 b}{7}+b=\frac{108}{7 \times 2}$
$\frac{30 }{7}+b=\frac{108}{7 \times 2}$
$\frac{30}{7}+b=\frac{54}{7}$
$b=\frac{54}{7}-\frac{30}{7}$
$b=\frac{24}{7}$
$b=3 \frac{3}{7} m$
Question 9
Rahul had a rope of $325\frac{4}{5}$ m long. He cut off a $150\frac{3}{5}$ m long piece, then he divided the rest of the rope into 3 parts of equal length. Find the length of each part.
Sol :
Total length of rope = $325 \frac{4}{5} m$
Rahul cut off $150 \frac{3}{5} \mathrm{~m}$ of rope
Remaining length of rope = $325 \frac{4}{5}-150 \frac{3}{5}$
$=\frac{1629}{5}-\frac{753}{5}$
$=\frac{876}{5} \mathrm{~m}$
$=\frac{876}{5} \mathrm{~m}$
Rahul made remaining rope into 3 equal parts
$\begin{aligned} \therefore \text { length of each part } &=\frac{876}{5} \div \frac{3}{1} \\ &=\frac{876}{5} \times \frac{1}{3}=\frac{292}{5}=58 \frac{2}{5} \mathrm{~m} \\ \therefore \text { length of each part } & \text { part }=58 \frac{2}{3} \mathrm{~m} \end{aligned}$
Question 10
If $3\frac{1}{2}$ litre of petrol costs ₹ $270\frac{3}{8}$, then find the cost of 4 litre of petrol.
Sol :
$3 \frac{1}{2}$ liters of petrol cost= ₹ $270 . \frac{3}{8}$
cost for 1 liter of petrol $=\frac{270 \frac{3}{8}}{3 \frac{1}{2}}$
$=\frac{2163}{8} \times \frac{2}{7}$
Cost for 1 liter of petrol $=\frac{309}{4}$
cost for 4 liters of petrol $=\frac{309}{4} \times 4$
$\therefore$ cost for 4 liters of petrol = ₹ 309
Question 11
Ramesh earns ₹ 40,000 per month. He spends $\frac{3}{8}$ of the income on food, $\frac{1}{5}$ of the remaining on LIC premium and then $\frac{1}{2}$ of the remaining on other expenses. Find how much money is left with him?
Sol :
Ramesh Spends $\frac{3}{8}$ of income on food $=\frac{3}{8} \times 40000$
=15000
Remaining money =40000-15000
=25000
remaining spend $\frac{1}{5}$ of remaining on LIC
$=\frac{1}{5}(25000)$
$=5000$
Remaining money $=25000-195000$
$=20000$
other expenses are $\frac{1}{2} of$ remaining money
= $=\frac{1}{2} \times 20000$
= 10,000
$\begin{aligned} \text { Remaining money } &=20,000-10,000 \\ &=10,0001\end{aligned}$
Question 12
A, B, C, D and E went to a restaurant for dinner. A paid $\frac{1}{2}$ of the bill, B paid $\frac{1}{5}$ of the bill and rest of the bill was shared equally by C, D and E. What fraction of the bill was paid by each?
Sol :
Let total bill Amount as x
Amount paid A will be $=\frac{x}{2}$
Amount paid B will be $=\frac{x}{5}$
Amount paid C, D,E will be
$=x-\left(\frac{x}{2}+\frac{x}{5}\right)$
$=x-\left(\frac{5x+2x}{10}\right)$
$=x-\left(\frac{7x}{10}\right)$
$=\left(\frac{10x-7x}{10}\right)$
$=\left(\frac{3x}{10}\right)$
given bill is shared equally among three
Let bill paid by each one = y
$y+y+y=\frac{3x}{10}$
$3y=\frac{3x}{10}$
$y=\frac{x}{10}$
$y=\frac{1}{10}\times x$
$\therefore$ Each paid $\frac{1}{10}$ th of total bill.
Question 13
$\frac{2}{5}$ of total number of students of a school come by car while $\frac{1}{4}$ of students come by bus to school. All the other students walk to school of which $\frac{1}{3}$ walk on their own and the rest are escorted by their parents. If 224 students come to school walking on their own, how many students study in the school?
Sol :
no. of students of school come by car $=\frac{2}{5} x$
no. of Students of school come by bus e $\frac{1}{4} x$
no of students of school come by walk $=x-\left(\frac{2}{5} x+\frac{1}{4} x\right)$
$= x- \left(\frac{(2 \times 4)+(1 \times 5)}{20} \cdot x\right)$
$=x-\frac{13}{20} \cdot x$
no. of students of school come by walk $=\frac{7}{20} \cdot x$
no. of students of school come by walk on their own
$\begin{aligned} &=\frac{1}{3} \ of \left(\frac{7}{20} x\right) \\ &=\frac{7}{60} \cdot x \end{aligned}$
$\begin{aligned} \therefore \quad \frac{7}{60} \cdot x &=224 \\ x &=\frac{224}{1} \times \frac{60}{7} \\ x &=1920 \\ \text { Total Students in school }=1920 \end{aligned}$
Question 14
A mother and her two sons got a room constructed for ₹ 60,000. The elder son contributes $\frac{3}{8}$ of his mother’s contribution while the younger son contributes $\frac{1}{2}$ of his mother’s share. How much do the three contribute individually?
Sol :
Total cost of Room = ₹ 60,000
let Mother's contribution = ₹ x
Elder son contribution $= ₹ \frac{3}{8} x$
younger son contribution $= ₹ \frac{1}{2} x$
$\begin{aligned} \therefore \quad x+\frac{3}{8} x+\frac{1}{2} x &=60,000 \\ \frac{( 8)+(3)+(4)}{8} \cdot x &=60,000 \\ \frac{15}{8} \cdot x &=60000 \\ x &=60000 \times \frac{8}{15} \\ x &=32000 \end{aligned}$
; Mother's contribution =32,000
; Elder son's contribution e $\frac{3}{8} \times 32000=₹ 12,000$
; Younger son's Contribution = $\frac{1}{2} \times 32000=₹ 16,000$
Question 15
In a class of 56 students, the number of boys is $\frac{2}{5}$ th of the number of girls. Find the number of boys and girls.
Sol :
Total students =56
let no.of girls =x
no. of boys $=\frac{2}{5} x$
$\therefore \quad x+\frac{2}{5} x=56$
$\frac{7}{5} x=56$
$x=\frac{56}{1} \times \frac{5}{7}$
x=40
$\therefore$ no. of girls =40
$\therefore$ no. of boys =56-40=16
Question 16
A man donated $\frac{1}{10}$ of his money to a school, $\frac{1}{6}$ th of the remaining to a church and the remaining money he distributed equally among his three children. If each child gets ₹ 50000, how much money did the man originally have?
Sol :
Let money posses by man 2x
$\frac{1}{10}$th money donated to school $=\frac{x}{10}$
Remaining money $=x-\frac{x}{10}=\frac{9 x}{10}$
$\frac{1}{6}$th remaining money $=\left(\frac{9 x}{10}\right) \times \frac{1}{6}$
Remaining money $=\frac{9 x}{10}-\frac{9 x}{10 \times 6}$
$=\frac{45 x}{60}$
Now, man distributed This money equally to hin three sons and each one gets $=₹50,000$
$\frac{45 x}{60} \div 3=50,000$
$\frac{45 x}{60} \times \frac{1}{3}=50000$
$\frac{3}{4} x \times \frac{1}{8}=50000$
$x=50000 \times 4$
x=2,00,000
Question 17
If $\frac{1}{4}$ of a number is added to $\frac{1}{3}$ of that number, the result is 15 greater than half of that number. Find the number.
Sol :
Let a number be 'x'
$\frac{1}{4}$ of a number is added to $\frac{1}{3}$ of number
$\frac{x}{4}+\frac{x}{3}$ is 15 greater thaw half of number
$\begin{aligned} \frac{x}{4}+\frac{x}{3}=15 &+\frac{x}{2} \\ \frac{7 x}{12}=15 &+\frac{x}{2} \\ \frac{7 x}{12}-\frac{x}{2} &=15 \\ \frac{x}{12} &=15 \\ x &=15 \times 12 \\ x &=180 \end{aligned}$
Question 18
A student was asked to multiply a given number by $\frac{4}{5}$. By mistake, he divided the given number by $\frac{4}{5}$. His answer was 36 more than the correct answer. What was the given number?
Sol :
Let the number be 'x'
$\frac{x}{1} \div \frac{4}{5}=36+\left(x+\frac{4}{5}\right)$
$\frac{5 x}{4}=36+\frac{4 x}{5} .$
$\frac{5 x}{4}-\frac{4 x}{5}=36$
$\frac{(5 \times 5)-(4 \times 4)}{20} \cdot x=36$
$\frac{25-16}{20} \cdot x=36$
$\frac{9}{20} \cdot x=36$
$x=\frac{36}{9} \times 20$
x=80
$\therefore$ The given number is 80
No comments:
Post a Comment