Question 13 Marks
$10$ kg of sugar cost ₹ $350.$ If $x$ kg sugar of the same kind costs ₹ $175,$ find the value of $x$
Answer$10\ kg$ of sugar costs $= ₹ 350$ and
$x\ kg$ of sugar cost $= ₹ 175$
A.T.Q.
$10\ kg : xkg :: 350: 175$
$\Rightarrow 10 \times 175=350 \times x $
$\Rightarrow 350 x =1750$
$\Rightarrow x =\frac{1750}{350}=5$
Hence, $5\ kg$ of sugar costs $₹ 175$
View full question & answer→Question 23 Marks
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion?
Answer15 cm : 2 m :: 10 sec : 3 min
15 cm : 2 × 100 cm :: 10 sec : 30 × 60 sec
15 : 200 :: 10 : 1800
3 : 40 :: 1 : 180
No, they donot form a proportion
View full question & answer→Question 33 Marks
The ages of A and B are in the ratio 6 : 5. If A’s age is 18 years, find the age of B.
AnswerRatio in the ages of $A$ and $B=6: 5$
$A^{\prime}$ s age $=18$ years
Let $B^{\prime}$ s age $=x$ years
$6: 5=18: x$
$\Rightarrow \frac{6}{5}=\frac{18}{ x }$
$\Rightarrow 6 \times x=18 \times 5$
$\Rightarrow x=\frac{18 \times 5}{6}=15$
$\therefore$ B's age $=15$ years.
View full question & answer→Question 43 Marks
The ratio of the length and the width of a rectangular sheet of paper is 8 : 5. If the width of the sheet is 17.5 cm; find the length.
AnswerLet length of sheet $=x cm$
Ratio in length and breadth $=8: 5$
and width $=17.5 cm$
$8: 5=x: 17.5$
$\Rightarrow \frac{8}{5}=\frac{ x }{17.5}$
$\Rightarrow 8 \times 17.5=x \times 5$
$\Rightarrow x=\frac{8 \times 17.5}{5}=8 \times 3.5=28$
Length of sheet $=28 cm$
View full question & answer→Question 53 Marks
The costs of the two articles are in the ratio 7 : 4. If the cost of the first article is Rs. 2,800; find the cost of the second article.
AnswerRatio in the cost of two articles $=7: 4$
Cost of first article $=$ Rs. 2800
Let cost of the second article $=x$
$7: 4=2800: x$
$\Rightarrow \frac{7}{4}=\frac{2800}{ x }$
$\Rightarrow 7 \times x=2800 \times 4$
$\Rightarrow x =\frac{2800 \times 4}{7}=1600$
$\therefore$ Cost of second article $=$ Rs. 1600
View full question & answer→Question 63 Marks
Find the value of x of the following such that the given numbers are in proportion.
$45, 135, 90$ and $x$
Answer$\because 45,135,90$ and $x$ are in proportion
$\therefore \frac{45}{135}=\frac{90}{ x } $
$\Rightarrow 45 \times x=90 \times 135 $
$\Rightarrow x=\frac{90 \times 135}{45}=270$
$\therefore x=270$
View full question & answer→Question 73 Marks
Find the value of x of the following such that the given numbers are in proportion.
$14, 42, x$ and $75$
Answer$14,42, x$ and $75$ are in proportion
$\frac{14}{42}=\frac{x}{75} $
$\Rightarrow 14 \times 75=x \times 42$
$\Rightarrow x=\frac{14 \times 75}{42}=25$
$\therefore x=25$
View full question & answer→Question 83 Marks
If $25, 35$ and $x$ are in continued proportion, find the value of $x.$
Answer$25,35$ and $x$ are in continued proportion
$\Rightarrow 25: 35=35: x $
$\Rightarrow 25 \times x=35 \times 35 $
$\Rightarrow x=\frac{35 \times 35}{25} $
$\Rightarrow x=49$
View full question & answer→Question 93 Marks
Are the following numbers in proportion 12, 15, 18 and 20?
Answer$12,15,18$ and 20 are in proportion
if $12: 15=18: 20$
if $12 \times 20=15 \times 18 \ldots \ldots .\left\{\frac{a}{b}=\frac{c}{d} \Rightarrow a d=b c\right\}$
if $240=270$
which is not true.
$12,15,18$ and 20 are not in proportion.
View full question & answer→Question 103 Marks
If $4, x$ and $9$ are in continued proportion, find the value of $x.$
Answer$4, x$ and $9$ are in continued proportion
$\Rightarrow 4: x=x: 9 $
$\Rightarrow x^2=9 x 4 $
$\Rightarrow x=\sqrt{36} $
$x=6$
View full question & answer→Question 113 Marks
Are the following numbers in proportion 32, 40, 48 and 60?
Answer$32,40,48$ and 60 are in proportion
if $32: 40=48: 60$
if $32 \times 60=40 \times 48 \ldots \ldots\left\{\frac{a}{b}=\frac{c}{d} \Rightarrow ad = bc \right\}$
if $1920=1920$
Which is true.
$32,40,48$ and 60 are in proportion
View full question & answer→Question 123 Marks
$\text { If } \frac{2 y+5 x}{3 y-5 x}=2 \frac{1}{2}, \text { find } y \text {, if } x=33$
Answer$\frac{2 y+5 x}{3 y-5 x}=\frac{5}{2}$
Given $x=33$
$\frac{2 y+5 \times 33}{3 y-5 \times 33}=\frac{5}{2} $
$\Rightarrow \frac{2 y+165}{3 y-165}=\frac{5}{2}$
$\Rightarrow 2 \times(2 y+165)=5 \times(3 y-165)$
$\Rightarrow 4 y+330=15 y-825$
$\Rightarrow 11 y =1155$
$\Rightarrow y=\frac{1155}{11}=105$
View full question & answer→Question 133 Marks
$\text { If } \frac{2 y+5 x}{3 y-5 x}=2 \frac{1}{2}, \text { find } x \text {, if } y=70$
Answer$\frac{2 y+5 x}{3 y-5 x}=\frac{5}{2} $
$\text { Given } y=70 $
$\frac{2 \times 70+5 x}{3 \times 70-5 x}=\frac{5}{2} $
$\Rightarrow \frac{140+5 x}{210-5 x}=\frac{5}{2} $
$\Rightarrow 2 \times(140+5 x)=5 \times(210-5 x) $
$\Rightarrow 280+10 x=1050-25 x $
$\Rightarrow 35 x=1050-280 $
$\Rightarrow x=\frac{770}{35}=22$
View full question & answer→Question 143 Marks
$\text { If } \frac{2 y+5 x}{3 y-5 x}=2 \frac{1}{2} \text {, find } x: y$
Answer$\frac{2 y+5 x}{3 y-5 x}=\frac{2 \times 2+1}{2} $
$\frac{2 y+5 x}{3 y-5 x}=\frac{5}{2} $
$\Rightarrow 2 \times(2 y+5 x)=5 \times(3 y-5 x) $
$\Rightarrow 4 y+10 x=15 y-25 x $
$\Rightarrow 35 x=11 y $
$\Rightarrow \frac{x}{y}=\frac{11}{35}$
i.e. $x: y=11: 35$
View full question & answer→Question 153 Marks
If $(4x + 3y) : (3x + 5y) = 6 : 7,$ find y, if $x = 27$
Answer$(4 x+3 y):(3 x+5 y)=6: 7$
Given, $x=27$
$\therefore(4 \times 27+3 y):(3 \times 27+5 y)=6: 7 $
$(108+3 y):(81+5 y)=6: 7 $
$7 \times(108+3 y)=6 \times(81+5 y) $
$756+21 y=486+30\ y$
$9\ y=270$
$\Rightarrow y =\frac{270}{9}=30$
View full question & answer→Question 163 Marks
If $(4x + 3y) : (3x + 5y) = 6 : 7,$ find $x,$ if $y = 10$
Answer$(4 x+3 y):(3 x+5 y)=6: 7$
Given, $y=10$
$\therefore(4 x+3 \times 10):(3 x+5 \times 10)=6: 7 $
$(4 x+30):(3 x+50)=6: 7 $
$7 \times(4 x+30)=6 \times(3 x+50) $
$28 x+210=18 x+300 $
$28 x-18 x=300-210 $
$10 x=90 $
$\Rightarrow x=\frac{90}{10}=9$
View full question & answer→Question 173 Marks
If $(4x + 3y) : (3x + 5y) = 6 : 7,$ find $x : y$
Answer$7 x(4 x+3 y)=6 x(3 x+5 y) $
$28 x+21 y=18 x+30 y $
$28 x-18 x=30 y-21 y $
$10 x=9 y $
$\frac{x}{y}=\frac{9}{10} $
$\therefore x: y=9: 10$
View full question & answer→Question 183 Marks
Find the third proportional to $₹1.60, ₹0.40$
AnswerLet the required third proportional be $x$
$\therefore$ ₹1.60, ₹0.40, ₹$x$ are in continued proportion.
$\Rightarrow 1.60 \times x=0.40 \times 0.40 $
$\Rightarrow x=\frac{0.40 \times 0.40}{1.60} $
$\Rightarrow x=0.1$
$\therefore$ Required proportional $=0.1$
View full question & answer→Question 193 Marks
Find the third proportional to $5.25, 7$
AnswerLet the required third proportional be $x$
$\therefore 5.25,7, x$ are in continued proportion
$\Rightarrow 5.25: 7=7: x $
$\Rightarrow 5 x=7 \times 7 $
$\Rightarrow x=\frac{7 \times 7}{5.25} $
$\Rightarrow x=\frac{49}{5.25}=\frac{28}{3} $
$\Rightarrow x=9 \frac{1}{3}$
$\therefore$ Required proportional $=9 \frac{1}{3}$
View full question & answer→Question 203 Marks
Find the third proportional to $36, 18$
AnswerLet the required third proportional be $x$
$\therefore 36,18, x$ are in continued proportion
$\Rightarrow 36: 18=18: x $
$\Rightarrow 36 x=18 \times 18$
$\Rightarrow x =\frac{18 \times 18}{36}$
$\Rightarrow x =9$
$\therefore$ Required proportional $=9$
View full question & answer→Question 213 Marks
The ratio of copper and zinc in an alloy is $9 : 8.$ If the weight of zinc, in the alloy, is $9.6$ kg; find the weight of copper in the alloy.
AnswerLet the weight of copper $=x kg$
Weight of zinc $=9.6 kg$.
According to question,
$9: 8=x: 9.6 $
$\Rightarrow 8 \times x=9 \times 9.6 $
$\Rightarrow x=\frac{9 \times 9.6}{8}=9 \times 1.2=10.8 kg .$
Weight of copper in alloy $=10.8$
View full question & answer→Question 223 Marks
The ratio of the sale of eggs on a Sunday and that of the whole week at a grocery shop was $2 : 9.$ If the total value of the sale of eggs in the same week was $Rs 360,$ find the value of the sale of eggs that Sunday.
AnswerLet, the sale of eggs on Sunday $=x$
Sale in week $=$ Rs 360
According to question, $2: 9=x: 360$
$\Rightarrow 9 \times x=360 \times 2 $
$x=\frac{360 \times 2}{9}=\text { Rs } 80$
Sale on Sunday $= Rs 80$
View full question & answer→Question 233 Marks
The ratio of the length and the width of a school ground is $5 : 2.$ Find the length, if the width is $40$ metres.
Answer$\text { Let the length }=x m , $
$\text { width }=40 m $
$\text { The ratio of length to width }=x: 40 $
$\text { as per given statement } 5: 2=x: 40 $
$\Rightarrow 2 \times x=40 \times 5 $
$x=\frac{40 \times 5}{2}=20 \times 5=100\ m$
View full question & answer→Question 243 Marks
The first, second, and fourth terms of a proportion are $6, 18,$ and $75,$ respectively. Find its third term.
AnswerLet the third term $=x$
$6: 18:: x: 75$
$=18 \times x=6 \times 75$
$x=\frac{6 \times 75}{18}=\frac{75}{3}=25$
The third term of proportion is $25$
View full question & answer→Question 253 Marks
Make set of all possible proportions from the numbers 15, 18, 35 and 42.
AnswerThe possible proportions that can be made from the numbers 15, 18, 35 and 42 are
(i) 15 : 35 :: 18 : 42
(ii) 42 : 18 :: 35 : 15
(iii) 42 : 35 :: 18 : 15
(iv) 15 : 18 :: 35 : 42
View full question & answer→Question 263 Marks
The ratio of the number of girls to the number of boys in a school is $2 : 5.$ If the number of boys is $225;$ find:
(i) the number of girls in the school.
(ii) the number of students in the school.
AnswerLet, the number of girls in school $=x$
Number of boys in school $=225$
According to question $2: 5=x: 225$
$\Rightarrow 5 \times x=2 \times 225$
$x=\frac{2 \times 225}{5}=2 \times 45=90$
Number of girls in school $=90$
Total number of student in the school $=$ (number of boys + number of girls) $=(225+90)=$ 315
View full question & answer→