[2 Mark Question Answer]

Question 12 Marks

Decrease 275 in the ratio 11 : 7.

Answer

Given ratio $=11: 7$
The decrease quantity $=\frac{11}{7} \times$ given quantity.
$
=\frac{11}{7} \times 275=175
$

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Question 22 Marks

Increase 95 in the ratio 5 : 8.

Answer

Given ratio $=5: 8$
The increased quantity $=\frac{8}{5} \times$ given quantity
$=\frac{8}{5} \times 95=152$

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Question 32 Marks

An alloy of zinc and copper weighs $12 \frac{1}{2} kg$. if in the alloy, the ratio of zinc and copper is $1: 4$, find the weight of copper in it.

Answer

$\text { Weight of alloy }=12 \frac{1}{2} kg =\frac{25}{2} kg . $
$\text { Given ratio }=1: 4 $
$\text { Sum of ratio }=1+4=5 $
$\text { Weight of copper }=\frac{4}{5} \times \frac{25}{2} kg =2 \times 5=10\ kg$

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Question 42 Marks

Two numbers are in the ratio 9 : 2. If the smaller number is 320, find the larger number.

Answer

Let the larger number $=9 x$
and smaller number $=2 x$
If smaller number is 320 ,
then, larger number will be $=\frac{9 x \times 320}{2 x }=1440$

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Question 52 Marks

Reduce the following ratio to their lowest term:
$5$ kg $500$ gm $: 2$ kg $750$ gm

Answer

$5$ kg $500$ gm $: 2$ kg $750$ gm
$(5 \times 1000+500):(2 \times 1,000+750) \ldots \ldots . .(\because 1 kg =1,000 gm ) $
$=5500: 2750$
$=\frac{5,500}{2,750}=\frac{2}{1}=2: 1$

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Question 62 Marks

Reduce the following ratio to their lowest term:
$2$ m $40$ cm $: 1$ m $44$ cm

Answer

$2$ m $40$ m $: 1$ m $44$ cm
$=(2 \times 100+40):(1 \times 100+44) \ldots \ldots \ldots .(\because 1 m =100 cm ) $
$240: 144$
$=\frac{240}{144}=\frac{10}{6}=\frac{5}{3}=5: 3$

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Question 72 Marks

Reduce the following ratio to their lowest term:
$3$ years $4$ months $: 5$ years $5$ months.

Answer

$3 \text { years } 4 \text { months }: 5 \text { years } 5 \text { months }$
$=(3 \times 12+4):(5 \times 12+5) \ldots \ldots \ldots \ldots . .(\because 1 \text { year }=12 \text { months })$
$=40: 65$
$=\frac{40}{65}=\frac{8}{13}=8: 13$

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Question 82 Marks

The length of a pencil is 18 cm and its radius is 4 cm. Find the ratio of its length to its diameter.

Answer

Length of a pencil = 18 cm
Radius of a pencil = 4 cm
Diameter of a pencil = 2r = 2 × 4 = 8 cm
Ratio of length of a pencil to its diameter = 18 : 8 = 9 : 4

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Question 92 Marks

Express the following ratios in its simplest form :
$2.5 : 1.5$

Answer

$2.5: 1.5=\frac{25}{15}=\frac{5}{3}=5: 3 $
$\text { OR } 2.5: 1.5=\frac{25}{10}: \frac{15}{10}=\frac{25}{10} \div \frac{15}{10} $
$=\frac{25}{10} \times \frac{10}{15}=\frac{25}{15}=\frac{5}{3}=5: 3$

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Question 102 Marks

Express the following ratios in its simplest form :
$2 \frac{1}{3}: 3 \frac{1}{2}: 1 \frac{1}{4}$

Answer

$2 \frac{1}{3}: 3 \frac{1}{2}: 1 \frac{1}{4}=\frac{7}{3}: \frac{7}{2}: \frac{5}{4} $
$=\frac{7}{3} \times 12: \frac{7}{2} \times 12: \frac{5}{4} \times 12 \ldots \ldots . .(\text { L.C.M. of } 2,3 \text { and } 4=12) $
$=28: 42: 15$

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Question 112 Marks

Express the following ratios in its simplest form :
$4$ min $: 45$ sec

Answer

$4$ min $: 45$ sec $=240$ sec $=45$ sec
$(\because 1 \text { minutes }=60 sec , 4 \times 60=240 sec ) $
$\frac{240}{45}=\frac{16}{3}=16: 3$

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Question 122 Marks

Express the following ratios in its simplest form :
1 hour: 45 minutes

Answer

1 hour: 45 minutes $=60$ minutes $: 45$ minutes
$(\because 1$ hour $=60$ minutes $)$
$
\frac{60}{45}=\frac{4}{3}=4: 3
$

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Question 132 Marks

Express the following ratios in its simplest form :
2 years: 9 months

Answer

2 years : 9 months $=24$ months $: 9$ months
$(\because 2$ years $=2 \times 12$ months $=24$ months $)$ $=\frac{24}{9}
=\frac{8}{3}=8: 3$

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Question 142 Marks

Express the following ratios in its simplest form :
$3$ m $: 90$ cm

Answer

$3$ m $: 90$ cm $=300$ cm $: 90$ cm
$(\because 3 \times 100 cm =300 cm ) $
$\frac{300}{90}=\frac{10}{3}=10: 3$

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Question 152 Marks

Express the following ratios in its simplest form :
$30$ cm $: 2$ m

Answer

$30$ cm $: 2$ m $=30$ cm $: 2$ cm
$(\because 2 \times 100 cm =200 cm ) $
$\frac{30}{200}=\frac{3}{20}=3: 20$

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Question 162 Marks

Express the following ratios in its simplest form :
$5$ kg $: 800$ gm

Answer

$5 kg : 800 gm =5000: 800$
$(\because 5 \times 1000 gm =5000 gm ) $
$=\frac{5000}{800}=\frac{50}{5}=\frac{25}{4}=25: 4$

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