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Maths 2 Marks Questions

Ratio and Proportion · Uttarakhand Board (UBSE) STD 6 (Uttarakhand - English Medium). 19 questions.

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19 questions · timed · auto-graded

Question 12 Marks
In the following figure, each division represents $1\ cm:$

Express numerically the ratios of the following distances:
$i.\ AC : AF$
$ii.\ AG : AD$
$iii.\ BF : AI$
$iv.\ CE : DI$
Answer
$i.\ AC : AF = 2 : 5$
$ii.\ AG : AD = 2 : 1$
$iii.\ BF : AI = 1 : 2$
$iv.\ CE : DI = 2 : 5$
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Question 22 Marks
At the parking stand of Ramleela ground, Kartik counted that there are $115$ cycles, $75$ scooters and $45$ bikes. Find the ratio of the number of cycles to the total number of vehicles.
Answer
Given, at parking stand, number of Cycles $= 115$
Number of Scooters $= 75$
Number of Bikes $= 45$
Total number of vehicles $= 115 + 75 + 45 = 235$
Ratio of number of cycles to the total number of vehicles = $\frac{115}{235} =\frac{23}{47} =23:47$
$[$On dividing numerator and denominator by $5]$
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Question 32 Marks
A scooter travels $120\ km$ in $3$ hours and a train travels $120\ km$ in $2$ hours. Find the ratio of their speeds.(Hint: Speed = distance travelled time taken)
Answer
Scooter travels in $3h = 120\ km$
Speed of scooter = $\frac{\text{Distance }}{\text{Time}}=\frac{120}{3 }= 40\frac{\text{km}}{\text{h}}$
Train travels in $2h = 120\ km$
Speed of train $=\frac{120}{2 }= 60\frac{\text{km}}{\text{h}}$
Ratio of their speeds $=\frac{40}{60} = \frac{2}{3}= 2:3$
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Question 42 Marks
Which ratio is larger $10 : 21$ or $21 : 93?$
Answer
Given, ratios are $10 : 21$ and $21 : 93$
$\frac{10}{21}\ \text{and}​​\frac{21}{93}$
$10 \times 93$ and $21 \times 21 = 930$ and $441$
Hence, $10 : 21 > 21 : 93 10 : 21$ is larger then the ratio $21 : 93$
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Question 52 Marks
A line segment $56\ cm$ long is to be divided into two parts in the ratio of $2 : 5.$ Find the length of each part.
Answer
Given, Length of the line segment $= 56\ cm$
 Ratio of two parts $= 2 : 5$
 Sum of ratios $= 2 + 5 = 7$
Length of first part $=\frac{2}{7} \times 56=16\text{cm}$
Length of second part $=\frac{5}{7} \times 56=40\text{cm}$
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Question 62 Marks
An alloy contains only zinc and copper and they are in the ratio of $7 : 9.$ If the weight of the alloy is $8\ kg,$ then find the weight of copper in the alloy.
Answer
Given, the ratio of Zinc and
Copper in alloy $= 7 : 9$ and
weight of alloy $= 8\ kg$
Let the weight of Zinc and Copper in alloy be $7x$ and $9x$ respectively,
where $x$ is multiple of weight.
Then, total weight =$ 7x + 9x = 6x $
$16x = 8 \ kg$
$\Rightarrow\text{x} =\frac{1}{2}\text{kg}$
Weight of copper $= 9\text{x} = 9\times\frac{1}{2} = 4\frac{1}{2}\text{kg}$
Hence, the weight of copper is $4\frac{1}{2}\text{kg}$.
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Question 72 Marks
The number of milk teeth in human beings is $20$ and the number of permanent teeth is $32.$ Find the ratio of the number of milk teeth to the number of permanent teeth.
Answer
Number of milk teeth in human beings $= 20$ 
 Number of permanent teeth in human beings $= 32$
Ratio of the number of milk teeth to the number of permanent teeth $=\frac{20}{32}$ $=\frac{5}{8}$
$ [$On dividing numerator and denominator by $4] = 5 : 8$
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Question 82 Marks
The yield of wheat from $8$ hectares of land is $360$ quintals. Find the number of hectares of land required for a yield of $540$ quintals$?$
Answer
$\therefore 360$ quintals, wheat is yielded by $= 8$ hector
$\therefore 1 $ quintal wheat is yielded by $=\frac{ 8}{360}\text{hector}$
$\therefore 540$ quintals wheat will be yielded by $=\frac{ 8}{360}\times540$ $=12\ \text{hector}$
Hence, $540$ quintals will be yielded by $12$ hector.
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Question 92 Marks
In a floral design made from tiles each of dimensions $40\ cm$ by $60\ cm ($See Fig.$)$, find the ratios of:
$a.$ The perimeter of shaded portion to the perimeter of the whole design.
$b.$ The area of the shaded portion to the area of the unshaded portion.
Answer
Perimeter of shaded portion $= 10$ units
Perimeter of whole design $= 18$ units
Area of shaded portion $= 6sq$ units
Area of whole design $= 20sq$ units
Ratio of perimeter of shaded portion to the perimeter of the whole design $=\frac{10}{18} =\frac{5}{9} = 5:9$
Ratio of area shaded portion to the area of unshaded portion $=\frac{6}{(20-6)}=\frac{6}{14}=\frac{3}{7} = 3:7$
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Question 102 Marks
A car can travel $240\ km$ in $15$ litres of petrol. How much distance will it travel in $25$ litres of petrol$?$
Answer
Given, Distance travel by a car in $15L = 240\ km$
Distance travel by a car in $1L = \frac{240}{15} = 16\text{km}$
$\therefore$ Distance travel by a car in $25L = 16 \times 25 = 400\ km$
Hence, a car will travel $400\ km$ in $25L.$
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Question 112 Marks
The earth rotates $360^\circ $ about its axis in about $24$ hours. By how much degree will it rotate in $2$ hours$?$
Answer
$\therefore$ Earth rotates in $24h = 360^\circ $
$\therefore$ Earth rotates in $1h = \frac{360^\circ}{24}$
$\therefore$ Earth will rotate in $2h =\frac{360^\circ}{24}\times2 = 30^\circ$
Hence, Earth will rotate by $30^\circ $ in $2h.$
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Question 122 Marks
A rectangular sheet of paper is of length $1.2\ m$ and width $21\ cm.$ Find the ratio of width of the paper to its length.
Answer
Given, Length of rectangular sheet $= 1.2m [\because 1m = 100\ cm] = 1.2 \times 100\ cm = 120\ cm$
Width of rectangular sheet $= 21\ cm$
Ratio of width to length $= \frac{21\text{cm}}{120\text{cm}}$ = $\frac{7}{40} = 7:40$
$[$On dividing numerator and denominator by $3]$
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Question 132 Marks
Find two numbers whose sum is $100$ and whose ratio is $9 : 16.$
Answer
Let the two numbers are $9x$ and $16x,$ whose sum is $100. $
$\Rightarrow 9x + 16x = 100 $
$\Rightarrow 25x = 100$
$\Rightarrow x = 4$
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Question 142 Marks
Reshma prepared $18\ kg$ of Burfi by mixing Khoya with sugar in the ratio of $7 : 2.$ How much Khoya did she use$?$
Answer
Given, Quantity of Burfi $= 18\ kg$ and
Khoya : Sugar $= 7 : 2$
Total of ratio $= 7 + 2 = 9$
Quantity of Khoya = $\frac{18}{9} \times 7=14\text{kg}$
So, Reshma used $14\ kg$ Khoya.
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Question 152 Marks
Sex ratio is defined as the number of females per $1000$ males in the population. Find the sex ratio if there are $3732$ females per $4000$ males in a town.
Answer
$\text{Sex ratio}=\frac{\text{Number of females}}{\text{Number of males}}$
$=\frac{3732}{4000}$
$=\frac{933}{1000} [$On dividing numerator and denominator by $4]$
Hence, sex ratio is $933$ in the town.
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Question 162 Marks
In Fig. $(i)$ and Fig. $(ii),$ find the ratio of the area of the shaded portion to that of the whole figure:

Answer
From fig. $(i),$
Area of shaded portion $= 8sq$ units
Area of whole figure $= 16sq$ units
Ratio of area of the shaded portion to the whole figure $=\frac{8}{16} = \frac{1}{2} = 1:2$
From fig. $(ii),$
Area of shaded portion $= 8sq$ units
Area of whole figure $= 16sq$ units
Ratio of area of the shaded portion to the whole figure $=\frac{8}{16} = \frac{1}{2} = 1:2$
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Question 172 Marks
In a school, the ratio of the number of large classrooms to small classrooms is $3 : 4.$ If the number of small rooms is $20,$ then find the number of large rooms.
Answer
Given, ratio of number of large classrooms to small classrooms $= 3 : 4$
Number of small classrooms $= 20$
Let the classrooms are multiple of $x.$
So, large classrooms $= 3x$
Small classrooms $= 4x$
According to the question, $4x = 20$
$\Rightarrow\text{x}=\frac{20}{4}=5  . $
Hence, number of large classrooms =$ 3x = 3 \times 5 = 15$
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Question 182 Marks
A typist has to type a manuscript of $40$ pages. She has typed $30$ pages of the manuscript. What is the ratio of the number of pages typed to the number of pages left?
Answer
Total pages of manuscript to type $= 40$
Typed pages of manuscript $= 30$
Left pages $= 40 - 30 = 10$
Ratio of the number of pages to the types pages to the number of left pages $=\frac{30}{10} =\frac{3}{1} = 3:1$
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Question 192 Marks
When Chinmay visted chowpati at Mumbai on a holiday, he observed that the ratio of North Indian food stalls to South Indian food stalls is $5 : 4.$ If the total number of food stalls is $117,$ find the number of each type of food stalls.
Answer
Given, ratio of North Indian food stalls to South Indian food stalls $= 5 : 4$
Total number of food stalls $= 117$
Total ratio $= 5 + 4 = 9$
North Indian food stalls $=\frac{5}{9}\times117 = 65$
South Indian food stalls $=\frac{4}{9}\times117 = 52$
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