1 Marks Question

Question 11 Mark

Fill in the blank:If $9, x, x, 49$ are in proportion, then $x$ ......

Answer

If $9, x, x, 49$ are in proportion, then $x =$ 21
Given:
$25, 35 :: 35 : x$
Now, we know
Product of means = Product of extremes
$\text{x}\times\text{x}=9\times49$
$\text{x}^2=441$
$\text{x}^2=21^2$
$\text{x}=21$

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Question 21 Mark

Fill in the blank: If $25, 35\ x$ are inproportion, then $x =$ ......

Answer

If $25, 35\ x$ are inproportion, then $\text{x}=\frac{1225}{25}=49$
Given:
$25, 35 :: 35 : x$
Now, we know
Product of extremes = Product of means $25\times\text{x }=34\times35$
$\text{x}=1225$ $\text{x}=\frac{1225}{25}=49$

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Question 31 Mark

Fill in the place holders:
$\frac{24}{40}=\frac{\Box}{5}=\frac{12}{\Box}$

Answer

$\frac{24}{40}=\frac{3}{5}=\frac{12}{20}$
$5=40\div8$
$\frac{24}{40}=\frac{24\div8}{40\div8}=\frac{3}{5}$
$12=24\div2$
$=\frac{24\div2}{40\div2}=\frac{12}{20}$
Hence, $\frac{24}{40}=\frac{3}{5}=\frac{12}{20}$

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Question 41 Mark

Write $(T)$ for true and $(F)$ for false in case of the following:
$32\ kg : Rs. 36 :: 8\ kg : Rs. 9$

Answer

False.
The given statement is false as the terms of the ratio must have same units.

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Question 51 Mark

Fill in the blank: $\frac{14}{21}=\frac{\Box}{3}=\frac{6}{\Box}$

Answer

$\frac{14}{21}=\frac{2}{3}=\frac{6}{9}$
Let $\frac{14}{21}=\frac{\text{x}}{3}$ Thus,
we have: $21\text{x}=14\times3$
$\Rightarrow\text{x}=\frac{14\times3}{21}=2$
$\therefore\frac{14}{21}=\frac{2}{3}$ Again,
Let $\frac{2}{3}=\frac{6}{\text{y}}$ Thus,
we have: $2\text{y}=6\times3$
$\Rightarrow\text{y}=\frac{6\times3}{2}=9$
$\therefore\frac{2}{3}=\frac{6}{9}$
$\therefore\frac{14}{21}=\frac{2}{3}=\frac{6}{9}$

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Question 61 Mark

Write $(T)$ for true and $(F)$ for false in case of the following: $51 : 68 :: 85 : 102$

Answer

We have, $51 : 68=\frac{51}{68}=\frac{3}{4}$
$\text{And, }85:102=\frac{85}{102}=\frac{5}{6}$
$\therefore51:68\neq85:102$
So, the given statement in false.

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Question 71 Mark

Write $'T'$ for true and $'F'$ for false for the statements given below: $30, 40, 45, 60$ are in proportion.

Answer

True.
$30, 40, 45, 60$ $\frac{30}{40}=\frac{3}{4},\frac{45}{60}$
$=\frac{45\div15}{60\div15}=\frac{3}{4}$
They are in proportion Hence true.

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Question 81 Mark

Fill in the blank: If $36 : 81 :: x : 63$, then $x =$ ......

Answer

If $36 : 81 :: x : 63$, then $x =$ 28
If $36 : 81 :: x : 63$ Product of means = product of extremes
$81\text{x }=36\times63$ $\text{x}=\frac{2268}{81}$ $\text{x}=28$

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Question 91 Mark

Write $'T'$ for true and $'F'$ for false for the statements given below: $60p : Rs. 3 = 1 : 5$

Answer

True.
$60p : Rs. 3 = 60p : 300p$ $(1\ Re = 100p)$
$=\frac{60}{300}=\frac{6}{30}$
$=\frac{6\div6}{30\div6}=\frac{1}{5}$
Hence True.

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Question 101 Mark

Fill in the place holders: $\frac{5}{7}=\frac{\Box}{28}=\frac{35}{\Box}$

Answer

$\frac{5}{7}=\frac{20}{28}=\frac{35}{49}$
$\frac{5}{7}=\frac{\Box}{28}$
$\because28=7\times4$
$\therefore\frac{5}{7}=\frac{5\times4}{7\times4}=\frac{20}{28}$ $\text{and }\frac{5}{7}=\frac{35}{\Box}$
$\because35=5\times7$
$\frac{5}{7}=\frac{5\times7}{7\times7}=\frac{35}{49}$
$\therefore\frac{5}{7}=\frac{20}{28}=\frac{35}{49}$

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Question 111 Mark

Write $'T'$ for true and $'F'$ for false for the statements given below:A dozen : a score $= 5 : 3$

Answer

False.
$1$ dozen : $1$ score $= 12.20$
$=\frac{12}{20}$
$=\frac{6\div6}{20\div4}=\frac{3}{5}$
Hence False.

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Question 121 Mark

Fill in the place holders: $\frac{36}{63}=\frac{4}{\Box}=\frac{\Box}{21}$

Answer

$\frac{36}{63}=\frac{4}{7}=\frac{12}{21}$
$\frac{36}{63}=\frac{4}{\Box}=\frac{\Box}{21}$
$\frac{36}{63}=\frac{4}{\Box}$
$\therefore4=36\div9$
$\frac{36}{63}=\frac{36\div9}{63\div9}=\frac{4}{7}$
and $\frac{36}{63}=\frac{\Box}{21}$
$21=63+3$
$\therefore\frac{36}{63}=\frac{36\div3}{63\div3}=\frac{12}{21}$
$\therefore\frac{36}{63}=\frac{4}{7}=\frac{12}{21}$

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MCQ 131 Mark

Mark $(\checkmark)$ against the correct answer in the following: In covering $148\ km$, a car consumes $8$ litres of petrol. How many kilometers will it go in $10$ litres of pretrol?

A
$175\ km$
✓
$185\ km$
C
$205\ km$
D
$266.4\ km$

Answer

Correct option: B.

$185\ km$

Distance covered by a car in $8$ litres of petrol $= 148\ km$
Distance covered by it in $1$ litre of petrol $=\frac{148}{8}\text{km}$
Distance covered by it in litres of petrol $=10\times\frac{148}{8}$
$=\frac{148}{8}=185\text{ km}.$

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MCQ 141 Mark

Mark $(\checkmark)$ against the correct answer in the following: If $a, b, c$ are in proportion, then:

A
$ a^2=b c $
✓
$ b^2=a c $
C
$ c^2=a b $
D
None of these.

Answer

Correct option: B.

$ b^2=a c $

$a, b, c$ are in proportion, such that we have:
$a : b :: b : c$
Now, we know:
Product of means = Product of extremes
$b \times b = a \times c$
$b^2= ac$

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Question 151 Mark

Write $(T)$ for true and $(F)$ for false in case of the following: $81\ kg : 45\ kg :: 18$ men : $10$ men

Answer

True
We have, $81\ kg : 45\ kg = 81 : 45$ $=\frac{81}{45}=\frac{9}{5}$ And, $18$ men : $10$ men $=18:10$
$=\frac{18}{10}=\frac{9}{5}$
$\therefore81\text{kg}:45\text{kg}=18\text{ men}:10\text{ men}$
So, given statement is true.

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Question 161 Mark

Fill in the blank: $90\ cm : 1.5m = .....$

Answer

$90\text{cm}: 1.5\text{m} =\frac{3}{5}$
$90\ cm : 1.5m$
(or) $90\ cm : 1.50\ cm (1m = 10\ cm)$
$(H.C.F.$ of $9$ and $15$ is $3)$
$=\frac{90}{150}=\frac{9}{15}=\frac{9\div3}{15\div3}$
$=\frac{3}{5}$

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Question 171 Mark

Write $(T)$ for true and $(F)$ for false in case of the following: $45\ km : 60\ km :: 12h : 15h$

Answer

False.
We have, $45\ km : 60\ km$
$= 45 : 60$
$=\frac{45}{60}=\frac{3}{4}$
$\text{And}, 12\text{h} : 15\text{h}$
$=12:15$
$=\frac{12}{15}=\frac{4}{5}$
$\therefore45\text{km }60\text{km }\neq12\text{h}:15\text{h}$
So, the given statement is false.

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