1 Mark 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
Solution:
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 $\text{x}=\frac{1225}{25}=49$ Solution: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

$\frac{24}{40}=\frac{3}{5}=\frac{12}{20}$
Solution:
$5=40\div8$
$\frac{24}{40}=\frac{24\div8}{40\div8}=\frac{3}{5}$
$12=24\div2$
$=\frac{24\div2}{40\div2}=\frac{12}{20}$
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:
32kg : Rs. 36 :: 8kg : Rs. 9

Answer

False.
Solution:
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

$\frac{14}{21}=\frac{2}{3}=\frac{6}{9}$
Solution:
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.
Solution:
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
Solution:
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.Solution:
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

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

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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.Solution:
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

$\frac{36}{63}=\frac{4}{7}=\frac{12}{21}$Solution:
$\frac{36}{63}=\frac{4}{\Box}=\frac{\Box}{21}$
$\frac{36}{63}=\frac{4}{\Box}$
$\therefore4=36\div9$
$\frac{36}{63}=\frac{36\div9}{63\div9}=\frac{4}{7}$
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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Question 131 Mark

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

175km
185km
205km
266.4km

Answer

185km

Solution:

Distance covered by a car in 8 litres of petrol = 148km

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
$a^2 = bc$
✓
$b^2 = ac$
C
$c^2 = ab$
D
None of these.

Answer

Correct option: B.

$b^2 = ac$

$a, b, c$ 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:
81kg : 45kg :: 18 men : 10 men

Answer

True
Solution:
We have, 81kg : 45kg
= 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:
90cm : 1.5m = .....

Answer

$90\text{cm}: 1.5\text{m} =\frac{3}{5}$Solution:
90cm : 1.5m
(or) 90cm : 1.50cm (1m = 10cm)
(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:
45km : 60km :: 12h : 15h

Answer

FalseSolution:
We have, 45km : 60km
= 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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Maths 1 Mark Question

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