2 Mark Question

Question 12 Marks

If 48 boxes contain 6000 pens, how many such boxes will be needed for 1875 pens?

Answer

6000 pens by contain = 48 boxes
1 pens by contain $=\frac{48}{6000}$ boxes [less pen, less box]
1875 pens by contain $=\frac{48}{6000}\times1875=15\text{ boxes}$
Hence, 15 boxes will be needed for 1875 pens.

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Question 22 Marks

Determine if the following numbers are in proportion:
4, 6, 8, 12

Answer

4, 6, 8, 12
If it is in proportion, then
If ad = bc if 4 × 12 = 6 × 8
If 48 = 48
Which is true
$\therefore$ 4, 6, 8, 12 are in proportion

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Question 32 Marks

Verify the following:
39 : 65 :: 141 : 235

Answer

We have 39 : 65 :: 141 : 235
Product of means = 65 × 141 = 9165
Product of extremes = 39 × 235 = 9165
$\therefore$ Product of means = Product of extremes
Hence 39 : 65 :: 141 : 235 is verified.

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Question 42 Marks

Cost of 4 dozen bananas is Rs. 104. How many bananas can be purchased for Rs. 6.50?

Answer

In Rs. 104 buy of bananas = 4 dozen = 48
In Rs. 1 buy of bananas $=\frac{48}{104}$ [less rupee, less bananas]
In Rs. 6.50 Buy of bananas $=\frac{48}{104}\times\frac{650}{100}=3$
Hence, 3 bananas can be purchase f or Rs. 6.50.

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Question 52 Marks

The cost of 18 chairs is Rs. 22770. How many such chairs can be bought for Rs. 10120?

Answer

In Rs. 22770 bought = 18 chairs
In Rs 1 bought $=\frac{18}{22770}\text{chairs}$ [less rupee, less chairs]
In Rs 10120 bought,
$=\frac{18}{22770}\times10120=8\text{ chairs}$
Hence, 8 chairs can be bought for Rs. 10120.

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Question 62 Marks

Find the following ratios in the simplest form:
1.8kg to 6kg

Answer

$1.8\text{kg to 6kg}=\frac{18}{10}:6$
$=18:60=\frac{18}{60}=\frac{18\div6}{60\div6}$
$(\text{HCF of 18, 60 = 6})$
$=\frac{3}{10}=3:10$

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Question 72 Marks

Determine if the following numbers are in proportion:
22, 33, 42, 63

Answer

22, 33, 42, 63 or 22 : 33 :: 42 : 63
Are in proportion
If ad = bc
If 22 × 63 = 33 × 42
If 1386 = 1386
Which is true
$\therefore$ 22, 33, 42, 63 are in proportion.

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Question 82 Marks

Find the following ratios in the simplest form:
4kg to 750g

Answer

4kg to 750g $= 4000\text{g} : 750\text{g}$ $=\frac{4000}{750}=\frac{4000\div250}{750\div250}$

$(\text{HCF of 4000 and 750 = 250})$ $=\frac{16}{3}=16:3$

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Question 92 Marks

4.5g of an alloy of copper and zinc contains 3.5g of copper. What weight of copper will there be in 18.9g of the alloy?

Answer

4.5g of an alloy contains = 3.5g
1g of an alloy contains $=\frac{3.5}{4.5}\text{g}$ [less alloy, less copper]
18.9g an alloy contains $=\frac{3.5}{4.5}\times18.9=14.7\text{g}$
Hence, 14.7g copper will there be in 18.9g of the of the alloy

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Question 102 Marks

Find the ratio of:
90cm to 1.05m

Answer

90cm : 1.0m (or) 90cm : 105cm (1m = 100cm)
$\frac{90}{105}=\frac{90\div15}{105\div15}=\frac{6}{7}$ (H.C.F of 90 and 105 is 15.)
$\therefore 6 :7 $

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Question 112 Marks

Determine if the following numbers are in proportion:
150, 200, 250, 300

Answer

150, 200, 250, 300 or
150 : 200 :: 250 : 300 are in proportion
If ad = bc if 150 × 300 = 200 × 250
If 45000 = 50000
Which is not true
$\therefore$ 150, 200,250, 300 are not in proportion

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Question 122 Marks

A transport company charges Rs. 540 to carry 25 tonnes of weight. What will it charge to carry 35 tonnes?

Answer

To carry 25 tonnes for charges = Rs. 540
To carry 1 tonnes for charges $\text{Rs. }\frac{540}{25}$ [less weight, less charges]
To carry 35 tonnes for charges $=\text{Rs. }\frac{540}{25}\times35=\text{Rs. }756$
Hence, the transpoort charges Rs. 756 to carry 35 tonnes

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Question 132 Marks

Verify the following:
91 : 104 :: 119 : 136

Answer

We have 91 : 104 :: 119 : 136
Product of means = 104 × 119 = 12376
Product of extremes = 91 × 136 = 12376
Product of means = Product of extremes
Hence 91 : 104 :: 119 : 136 is verified.

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Question 142 Marks

A labourer earns Rs. 1980 in 12 days.
In how many days will he earns Rs. 2640?

Answer

The labourer earns Rs. 1980 in 12 days
The labourer earns Rs. 1 in $\frac{12}{1980}$ days [less time, less earns]
The labourer earns Rs. 2640 $\frac{12}{1980}\times2640=16\text{ days}$
Hence, the labourer earns Rs. 2640 in 16 days.

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Question 152 Marks

If the cost of a dozen soaps is Rs. 285.60, what wil be the cost of 15 such soaps?

Answer

Cost of 12 soaps = Rs. 285.60Cost of 1 soap $=\text{Rs }\Big(\frac{285.60}{12}\Big)$ [less soap, less cost]
Cost of 15 soap $=\text{Rs. }\Big(\frac{28560}{12\times100}\times15\Big)=\text{Rs. }357$
Hence, the cost of 15 soaps is Rs. 357

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Question 162 Marks

A car travels 195km in 3 hours.How far will it travel in 7 hours with the same speed?

Answer

In 3 hours the car travel 195km
In 1 hours the car travel $\frac{195}{3}\text{km}$ [less time, less distance]]
In 7 hours the car travel $\frac{195}{3}\times7=455\text{km}$
Hence, 455km will the car travel in 7 hours.

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Question 172 Marks

If 22.5m of a uniform iron rod weighs 85.5kg, what will be the weight of 5m of the same rod?

Answer

Weight of 22.5m of uniform iron rod = 85.5kg
Weight of 1m iron rod is $=\Big(\frac{85.5}{22.5}\Big)\text{kg}$ [less iron less wieght]
Weight of 5m iron rod $=\Big(\frac{855\times10}{225\times10}\times5\Big)=19\text{kg}$
Hence, the weight of 5m rod is 19kg

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Question 182 Marks

The weight of 65 books is 13kg.What is the weight of 80 such books?

Answer

The wieght of 65 books = 13kg
The wieght of 1 book $=\frac{13}{65}\text{kg}$ [less book, less weight]
The wieght of 80 books $=\frac{13}{65}\times80=16\text{kg}$
Hence, the wieght of 80 books is 16kg.

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Question 192 Marks

If 15 tins of the same size contain 234kg of oil, how much oil will there be in 10 such tins?

Answer

Oil contained by 15 tins = 234kg
Oil contained by 1 tin $=\Big(\frac{234}{15}\Big)\text{kg}$ oil [less tin, less oil]
10 tin contain $=\Big(\frac{234}{15}\times10\Big)=156\text{kg oil}$
Hence, 156kg oil will there in 10 tins.

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Question 202 Marks

Find the ratio of:
150mL to 2L

Answer

150mL to 2L (or) 150L : 2000L (1L = 1000mL)
$\frac{150}{2000}=\frac{150\div50}{2000\div50}=\frac{3}{40}$ (HCF of 150 and 2000 is 50)
$\therefore3:40$

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Question 212 Marks

24 workers can build a wall in 15 days. how many days will 9 workers take to build similar wall?

Answer

24 workers build the wall in 15 days
1 workes build the wall in 24 × 15 days [less worker, more time]
9 workers build wall in $\frac{24\times15}{9}=40\text{ days}$
Hence, 9 workers take to build the wall in 40 days.

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Question 222 Marks

Find the following ratios in the simplest form:
48 minutes to 1 hour

Answer

48 minutes to 1 hour
= 48 minutes : 60 minutes
= 48 : 60 = 4 : 5

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Question 232 Marks

Find the valueof x if 5 : 3 :: x : 6.

Answer

5 : 3 :: x : 6
$\because\text{ad}=\text{bc}$
$\therefore5\times6=3\times\text{x}$
$\Rightarrow\text{x}=\frac{5\times6}{3}=10$
$\therefore\text{x}=10$

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Question 242 Marks

A car travels 195km in 3 hours.How long will it take a travel 520km?

Answer

The car travel 195km in 3 hours
The car travel 1km in $\frac{3}{195}$ hours [less distance, less time]
The car travel 520km in $\frac{3}{195}\times520=8\text{ hour}$
Hence, the car travel 520km in 8 hours.

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Question 252 Marks

The weight of 65 books is 13kg.
How many such books weigh 6.4kg?

Answer

13kg weight = 65 books
1kg weight $=\frac{65}{13}$ books [less weight, less book]
6.4kg weight $=\frac{65}{13}\times6.4=32\text{ books}$
Hence, 32 books weigh 6.4kg.

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Question 262 Marks

If 9kg of rice costs Rs. 327.60, what will be the cost of 50kg of rice?

Answer

Cost of 9kg of rice = Rs. 327.60
Cost of 1kg of rice $\text{Rs }\Big(\frac{327.60}{9}\Big)$ [less rice, less cost]
cost of 50kg rice $=\text{Rs }\Big(\frac{32760}{9\times100}\times50\Big)=\text{Rs. }1820$
Hence, the cost of 50kg rice is Rs. 1820.

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Question 272 Marks

35 inland letters cost Rs. 87.50. How many such letters can we buy for 315?

Answer

For Rs. 87.50 buy = 35 letters
For Rs. 1 buy $=\frac{35}{87.50}$ letters [less rupee, less letters]
For Rs. 315 $=\frac{35\times100}{8750}\times315=126$ letters
Hence, 126 letters can we buy for Rs. 315

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Question 282 Marks

Verify the following:
108 : 72 :: 129 : 86

Answer

We have 108 : 72 :: 129 : 86
Product of means = 72 × 129 = 9288
Product of extremes = 108 × 86 = 9288
Product of means = Product of extremes
Hence 108 : 72 :: 129 : 86 is verified.

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Question 292 Marks

Find the ratio of:
2 dozens to a score

Answer

2 dozes to a score (or) 24 : 20 (1 dozen = 12 and 1 score = 20)
$\frac{24}{20}=\frac{24\div4}{20\div4}=\frac{6}{5}$ (H.C.F of 24 and 20 is 4)
$\therefore6:5$

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Question 302 Marks

Find the following ratios in the simplest form:
2.4km to 900m

Answer

$2.4\text{km to 900m}$
$=2400\text{m}:900\text{m}=\frac{2400}{900}$
$=\frac{2400\div300}{900\div300}$
$(\text{HCF of 2400 and 900 = 300})$
$=\frac{8}{3}=8:3$

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Question 312 Marks

Find the following ratios in the simplest form:
84 paise to Rs. 3

Answer

84 paise to Rs. 3
$=84\text{p}:300\text{p}$
$=\frac{84}{300}=\frac{84\div12}{300\div12}$
(HCF of 84 and 300 = 12)
$=\frac{7}{25}=7:25$

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Question 322 Marks

Verify the following:
60 : 105 :: 84: 147

Answer

We have 60 : 105 :: 84 : 147
Product of means = 105 × 84 = 8820
Product of extremes = 60 × 147 = 8820
$\therefore$ Product of means = Product of extremes
Hence 60 : 105 :: 84 : 147 is verified.

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Question 332 Marks

A labourer earns Rs. 1980 in 12 days.
How much does he earn in 7 days?

Answer

In 12 days the labourer earns = Rs. 1980
In 1 days the labourer earns $=\text{Rs. }\frac{1980}{12}$ [less time, less earn]
In 7 days the labourer earns $=\text{Rs. }\frac{1980}{12}\times7=\text{Rs. }1155$
Hence, the labourer earns Rs. 1155 in 7 days.

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Question 342 Marks

Find the followlng ratios in the simplest form:
24 to 56

Answer

24 to 56
$=\frac{24}{56}$
$=\frac{24\div8}{56\div8}$
(HCF of 24, 56 = 8)
$=\frac{3}{7}=3:7$

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Question 352 Marks

Determine if the following numbers are in proportion:
32, 48, 70, 210

Answer

32, 48, 70, 210 or 32 : 48 :: 70 : 210
Are in proportion
If ad = bc
If 32 × 210 = 48 × 70
If 6720 = 3360
Which is not true
$\therefore$ 32, 48, 70, 210 are not in proportion

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Question 362 Marks

In an army camp, there were provisions for 550 men for 28 days. But, 700 men attended the camp. How long did the provisions last?

Answer

550 men have provisions for 28 days
1 men have provisions for 28 × 550 days [less men, more days]
700 men have provisions for $\Big(\frac{28\times550}{700}\Big)=22\text{ days}$
Hence, 22 days did the provisions last.

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Question 372 Marks

If the cost of 14m of cloth is Rs. 1890, find the cost of 6m of cloth.

Answer

Cost of 14m of cloth = Rs. 1890
Cost of 1m of cloth $=\Big(\frac{1890}{14}\Big)=\text{Rs. }135$
Cost of 6m of cloth $=\text{Rs. }\Big(\frac{1890}{14}\times6\Big)=\text{Rs. }810$
Hence, the cost of 6m cloths is Rs. 810

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Question 382 Marks

Determine if the following numbers are in proportion:
33, 121, 9, 96

Answer

33, 121, 9, 96 or 33 : 121 :: 9 : 96
Are in proportion
If ad = bc
If 33 × 96 = 121 × 9
If 3168 = 1089
Which is not true
$\therefore$ 33, 121,9, 96 are not in proportion

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Question 392 Marks

A given quantity of rice is sufficient for 60 persons for 3 days. How many days would the rice last for 18 persons?

Answer

60 persions eat the rice in 3 days.
1 persons eat the rice in (3 × 60) days [less persons, more time]
18 persons eat the rice in $\Big(\frac{3\times60}{18}\Big)= 10\text{ days}$
Hence, 10 days would the rice last for 18 persons.

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Question 402 Marks

If 12L of diesel is consumed by a car in covering a distance of 222km, how many kilometres will it go in 22L of diesel?

Answer

12L of diesel consumed by distance = 222km
1L of diesel consumed by distance $=\frac{222}{12}\text{km}$
22L diesel consumed by distance $=\frac{222}{12}\times22=407\text{km}$
Hence, 407km will the car go in 22L diesel.

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Question 412 Marks

40 men can finish a piece of work in 26 days. How many men will be needed to finish it in 16 days?

Answer

In 26 days the work finished by 40 men
In 1 days the work finished by 40 × 26 men [less time, more men]
In 16 days the work finished by $\frac{40\times26}{16}=65\text{ men}$
Hence, 65 men will be needed to finish th work in 16 days.

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Question 422 Marks

Find the ratio of:
35 minutes to an hour

Answer

35 minutes to an hour (or) 35 minutes 60 minutes (1 hour = 60 minutes)
$\frac{36}{60}=\frac{35\div5}{60\div5}=\frac{7}{12}$ (H.C.F of 35 and 60 is 5)
$\therefore7:12$

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Question 432 Marks

Determine if the following numbers are in proportion:
7, 42, 13, 78

Answer

7, 42, 13, 78
7 : 42 :: 13 : 78
If ad = bc if 7 × 78 = 42 × 13
If 546 = 546
Which is true
$\therefore$ 7, 42, 13, 78 are in proportion.

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