[3 marks sum]

Question 13 Marks

The number 650 is decreased to 500 in the ratio a : b, find the ratio a : b.

Answer

The given quantity $=650$
and the decreased quantity $=500$
The ratio ( $a$ : b) by which 650 is decreased to $500=\frac{650}{500}=\frac{13}{10}$
The resulting ratio $=13: 10$

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Question 23 Marks

Increase 1200 in the ratio 3 : 7 and then increase the resulting number again in the ratio 4 : 7.

Answer

The given quantity $=1200$ increase in the ratio is $3: 7$
The increased quantity $=\frac{7}{3} \times 1200=2800$
Now, the quantity is increased again in the ratio $4: 7$
The resulting quantity $=\frac{7}{4} \times 2800=4900$

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Question 33 Marks

Increase 1200 in the ratio 2 : 3 and then decrease the resulting number in the ratio 10 : 3.

Answer

The given quantity $=1200$ and increase in the ratio is $2: 3$
The increased quantity $=\frac{3}{2} \times 1200=1800$
Now, the quantity is decrease in the ratio $10: 3$
$
=\frac{3}{10} \times 1800=540
$

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Question 43 Marks

Decrease 850 in the ratio 17 : 6 and then decrease the resulting number again in 4 : 3.

Answer

The given quantity $=850$ and decrease in the ratio $=17: 6$
The decreased quantity $=\frac{6}{17} \times 850=300$
Now, the quantity is decreased again in the ratio $=4: 3$
The resulting quantity $=\frac{3}{4} \times 300=225$

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Question 53 Marks

Decrease 850 in the ratio 17 : 6 and then increase the result in ratio 5 : 9.

Answer

The given quantity $=850$ and a decrease in the ratio $=17: 6$
The decreased quantity $=\frac{6}{17} \times 850=300$
Now, the quantity is increased in the ratio $5: 9$
The resulting quantity $=\frac{9}{5} \times 300=540$

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Question 63 Marks

Which ratio is smaller:
$\frac{7}{15} \text { or } \frac{15}{32}$

Answer

$\frac{7}{15} \text { or } \frac{15}{32} $
$\Rightarrow 7 \times 32 \text { or } 15 \times 15$
$\Rightarrow 224 \text { or } 225$
Since, $224<225$
$\therefore \frac{7}{15}$ is smaller.

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Question 73 Marks

Which ratio is smaller:
$\frac{9}{17} \text { or } \frac{8}{15}$

Answer

$\frac{9}{17} \text { or } \frac{8}{15} $
$\Rightarrow 9 \times 15 \text { or } 17 \times 8 $
$\Rightarrow 135 \text { or } 136$
Since, $135<136$
$\therefore \frac{8}{15}$ is smaller.

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Question 83 Marks

Which ratio is greater:
$\frac{3}{7} \text { or } \frac{6}{13}$

Answer

$\frac{3}{7} \text { or } \frac{6}{13}$
$\Rightarrow 3 \times 13 \text { or } 7 \times 6 $
$\Rightarrow 39 \text { or } 42$
Since, $42>39$
$\therefore \frac{6}{13}$ is greater.

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Question 93 Marks

Which ratio is greater:
$\frac{8}{15} \text { or } \frac{5}{9}$

Answer

$\frac{8}{15} \text { or } \frac{5}{9} $
$\Rightarrow 8 \times 9 \text { or } 15 \times 5 $
$\Rightarrow 72 \text { or } 75$
Since, $75>72$
$\therefore \frac{8}{15}$ is greater.

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Question 103 Marks

The number 800 is increased to 960 in the ratio a : b, find the ratio a : b.

Answer

The given quantity $=800$
and the increased quantity $=960$
The ratio (a : b) by which 800 is increased to $960=\frac{800}{960}=\frac{5}{6}$
The resulting ratio $=5: 6$

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Question 113 Marks

The sides of a triangle are in the ratio 3 : 2 : 4. If the perimeter of the triangle is 27 cm, find the length of each side.

Answer

Ratio in the sides of a triangle $=3: 2: 4$
Sum of ratios $=3+2+4=9$
Perimeter of triangle $=27 cm$
Length of first side $=\frac{27 \times 3}{9}=9 cm$
Length of second side $=\frac{27 \times 2}{9}=6 cm$
Length of third side $=\frac{27 \times 4}{9}=12 cm$

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Question 123 Marks

The angles of a triangle are in the ratio $3 : 7 : 8.$ Find the greatest and the smallest angles.

Answer

$\text { Sum of angles of triangle }=180^{\circ} $
$\text { Given ratio } 3: 7: 8 $
$\text { Sum of ratio }=3+7+8=18 $
$\text { Smallest angle }=\frac{3}{18} \times 180^{\circ}=30^{\circ} $
$\text { Greatest angle }=\frac{8}{18} \times 180^{\circ}=80^{\circ}$

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Question 133 Marks

Divide 81 into three parts in the ratio 2 : 3 : 4.

Answer

Given ratio $=2: 3: 4$
Sum of ratio $=2+3+4=9$
1 st part $=\frac{2}{9} \times 81=18$
2nd part $=\frac{3}{9} \times 81=27$
3rd part $=\frac{4}{9} \times 81=36$

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Question 143 Marks

$\text { Divide } 72 \text { in the ratio } 2 \frac{1}{2}: 1 \frac{1}{2}$

Answer

$\text { Given ratio }=2 \frac{1}{2}: 1 \frac{1}{2}=\frac{5}{2}: \frac{3}{2} $
$=\frac{5}{2} \times 2: \frac{3}{2} \times 2 $
$\text { Sum of ratio }=5+3=8 $
$\text { 1st divide }=\frac{5}{8} \times 72=45 $
$\text { 2nd divide }=\frac{3}{8} \times 72=27$

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Question 153 Marks

₹120 is to be divided between Hari and Gopi in the ratio 5 : 3. How much does each get?

Answer

Total amount = ₹ 120
Ratio in Hari and Gopi $=5: 3$
Sum of ratios $=5+3=8$
Hari's share $=\frac{120 \times 5}{8}$ = ₹75
and Gopi's share $=\frac{120 \times 3}{8}$ = ₹45

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Question 163 Marks

A bus travels 180 km in 3 hours and a train travels 450 km in 5 hours. Find the ratio of speed of train to the speed of bus.

Answer

Distance travelled by bus $=180 km$
Time taken $=3$ hours
$
\text { Speed }=\frac{\text { Distance }}{\text { Time }}=\frac{180}{3}=60 km / hr
$
Distance travelled by train $=450 km$
Time taken $=5$ hours
$
\text { Speed }=\frac{\text { Distance }}{\text { Time }}=\frac{450}{5}=90 km / hr
$
Ratio of speed of the train to the speed of bus $=90: 60=3: 2$

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Question 173 Marks

Reduce the following ratio to their lowest term:
4 weeks : 49 days

Answer

4 weeks : 49 days $=(4 \times 7)$ days : 49 days $(\because 1$ week $=7$ days $)$
$
=28: 49
$
$
=\frac{28}{49}
$
$
=4: 7
$

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Question 183 Marks

Reduce the following ratio to their lowest term:
1 hour 20 min : 2 hours

Answer

1 hour $20 min : 2$ hour
$=(1 \times 60+20)$ minutes: $2 \times 60$ minutes
$=80$ minutes $: 120$ minutes........$(\because 1$ hour $=60$ minutes $)$
$=\frac{80}{120}=\frac{2}{3}$
$=2: 3$

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Question 193 Marks

The weekly expenses of a boy have increased from ₹ 1,500 to ₹ 2,250. Find the ratio of:
(i) increase in expenses to original expenses.
(ii) original expenses to increased expenses.
(iii) increased expenses to increase in expenses.

Answer

Original expenses = ₹1500
Increased expenses =₹ 2250
Increase in expenses = ₹2250 - ₹1500 = ₹750
Now,
(i) Ratio in increase in expenses to original expenses = ₹750 : ₹1500=1: 2
(ii) Original expenses to increased expenses =₹ 1500 : ₹ 2250
$\frac{1500}{750}=\frac{2250}{750}=2: 3$
(iii) Increased expenses to increased in expenses = ₹ 2250 : ₹ 750 = 3: 1......(Dividing by $750)$

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Question 203 Marks

The strength of a class is 65, including 30 girls. Find the ratio of the number of:
(i) girls to boys
(ii) boys to the whole class
(iii) the whole class to girls

Answer

Total strength of class (including boys and girls) $=65$
Number of girls $=30$
Number of boys $=(65-30)=35$
(i) Ratio between girls and boys
$
=30: 35=\frac{30}{35}=\frac{6}{7}=6: 7
$
(ii) Ratio between boys and whole class
$
35: 65=\frac{35}{65}=\frac{7}{13}=7: 13
$
(iii) Ratio between whole class and girls
$
65: 30=\frac{65}{30}=\frac{13}{6}=13: 6
$

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Question 213 Marks

The monthly salary of a person is Rs. 12,000 and his monthly expenditure is Rs 8,500. Find the ratio of his:
(i) salary to expenditure
(ii) expenditure to savings
(ii) savings to salary

Answer

Monthly salary of a person $=$ Rs 12,000
Monthly expenditure $=8,500$
Saving of the person $=(12,000-8500)=$ Rs 3,500
(i) Ratio between salary and expenditure
$
12000: 8500=\frac{12000}{8500}=\frac{120}{85}=\frac{24}{17}=24: 17
$
(ii) Ratio between expenditure and saving
$
8500: 3500=\frac{8500}{3500}=\frac{85}{35}=\frac{17}{7}
$
(iii) Ratio between Savings and salary
$
3500: 12000=\frac{3500}{12000}=\frac{35}{120}=\frac{7}{24}=7: 24
$

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Question 223 Marks

Find the ratio between 5 dozen and 2 scores. [1 score = 20]

Answer

Ratio between 5 dozen and 2 scores
Given =1 score = 20
then, 2 scores = 2 × 20=40
and 1 dozen = 12,
5 dozen = 12 × 5 = 60
Then, ratio = 60 : 40 = 3 : 2

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Question 233 Marks

Find the ratio between 3.5 m, 475 cm and 2.8 m

Answer

The given values = 3.5 m, 475 cm and 2.8 m
= 3.5 x 100 cm : 475 cm : 2.8 x 100 cm
= 350 cm : 475 cm : 280 cm
= 70 cm : 95 cm : 56 cm
The ratio is 70 : 95 : 56

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Question 243 Marks

Is the ratio of 6 g and 15 g same as the ratio of 36 cm and 90 cm ?

Answer

Ratio of $6 g$ and $15 g$
$
=\frac{6}{15}=\frac{2}{5}=2: 5
$
Ratio of $36 cm$ and $90 cm$
$
=\frac{36}{90}=\frac{18}{45}=\frac{6}{15}=2: 5
$
Yes,the ratio in both cases are same.

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Question 253 Marks

Is the ratio of 15 kg and 35 kg same as the ratio of 6 years and 14 years?

Answer

Ratio of Weight $15 kg$ and $35 kg$
$
=\frac{15 kg }{35 kg }=\frac{3}{7}=3: 7
$
Ratio of 6 Years and 14 years
$
=\frac{6 \text { years }}{14 \text { years }}=\frac{3}{7}=3: 7
$
Yes, the ratio in both cases are same.

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MATHS [3 marks sum]

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