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.
View full question & answer→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 $ad = bc if 4 \times 12 = 6 \times 8$ If $48 = 48$ Which is true
$\therefore$ $4, 6, 8, 12$ are in proportion
View full question & answer→Question 32 Marks
Verify the following: $39 : 65 :: 141 : 235$
AnswerWe have $39 : 65 :: 141 : 235$
Product of means $= 65 \times 141 = 9165$
Product of extremes $= 39 \times 235 = 9165$
$\therefore$ Product of means = Product of extremes
Hence $39 : 65 :: 141 : 235$ is verified.
View full question & answer→Question 42 Marks
Cost of $4$ dozen bananas is $Rs. 104$. How many bananas can be purchased for $Rs. 6.50$?
AnswerIn $Rs. 104$ 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 $Rs. 6.50.$
View full question & answer→Question 52 Marks
The cost of $18$ chairs is $Rs. 22770$. How many such chairs can be bought for $Rs. 10120$?
AnswerIn $Rs. 22770$ 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 $Rs. 10120.$
View full question & answer→Question 62 Marks
Find the following ratios in the simplest form: $1.8\ kg$ to $6\ kg$
Answer$1.8\text{kg to 6\ kg}=\frac{18}{10}:6$
$=18:60=\frac{18}{60}=\frac{18\div6}{60\div6}$
$(\text{HCF of 18, 60 = 6})$
$=\frac{3}{10}=3:10$
View full question & answer→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 $22 \times 63 = 33 \times 42$
If $1386 = 1386$
Which is true
$\therefore$ $22, 33, 42, 63$ are in proportion.
View full question & answer→Question 82 Marks
Find the following ratios in the simplest form: $4\ kg$ to $750g$
Answer4kg to 750g $= 4000\text{g} : 750\text{g}$ $=\frac{4000}{750}=\frac{4000\div250}{750\div250}$
$(\text{HCF of 4000 and 750 = 250})$ $=\frac{16}{3}=16:3$ View full question & answer→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
View full question & answer→Question 102 Marks
Find the ratio of: $90\ cm$ to $1.05m$
Answer$90\ cm : 1.0m$ (or) $90\ cm : 105\ cm (1m = 100\ cm)$
$\frac{90}{105}=\frac{90\div15}{105\div15}=\frac{6}{7}$
$(H.C.F$ of $90$ and $105$ is $15.)$
$\therefore 6 :7 $
View full question & answer→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 $150 \times 300 = 200 \times 250$
If $45000 = 50000$
Which is not true
$\therefore$ $150, 200,250, 300$ are not in proportion
View full question & answer→Question 122 Marks
A transport company charges $Rs. 540$ to carry $25$ tonnes of weight. What will it charge to carry $35$ tonnes?
AnswerTo 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
View full question & answer→Question 132 Marks
Verify the following: $91 : 104 :: 119 : 136$
AnswerWe have 91 : 104 :: 119 : 136
Product of means $= 104 \times 119 = 12376$
Product of extremes $= 91 \times 136 = 12376$
Product of means = Product of extremes
Hence $91 : 104 :: 119 : 136$ is verified.
View full question & answer→Question 142 Marks
A labourer earns $Rs. 1980$ in 1$2$ days.
In how many days will he earns $Rs. 2640$?
AnswerThe 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.
View full question & answer→Question 152 Marks
If the cost of a dozen soaps is $Rs. 285.60$, what wil be the cost of $15$ such soaps?
AnswerCost of $12$ soaps $= Rs. 285.60$
Cost 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 $Rs. 357$
View full question & answer→Question 162 Marks
A car travels $195\ km$ in $3$ hours.How far will it travel in $7$ hours with the same speed?
AnswerIn $3$ hours the car travel $195\ km$ 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, $455\ km$ will the car travel in $7$ hours.
View full question & answer→Question 172 Marks
If $22.5m$ of a uniform iron rod weighs $85.5\ kg$, what will be the weight of $5m$ of the same rod?
AnswerWeight of $22.5m$ of uniform iron rod $= 85.5\ kg$
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 $19\ kg$
View full question & answer→Question 182 Marks
The weight of $65$ books is $13kg$.What is the weight of $80$ such books?
AnswerThe wieght of $65$ books $= 13\ kg$
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 $16\ kg.$
View full question & answer→Question 192 Marks
If $15$ tins of the same size contain $234\ kg$ of oil, how much oil will there be in $10$ such tins?
AnswerOil contained by $15$ tins $= 234\ kg$
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, $156\ kg$ oil will there in $10$ tins.
View full question & answer→Question 202 Marks
Find the ratio of: $150\ mL$ 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 $50)$
$\therefore3:40$
View full question & answer→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 $24 \times 15$ 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.
View full question & answer→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 $= 48 : 60 = 4 : 5$
View full question & answer→Question 232 Marks
Find the valueof $x$ if $5 : 3 :: x : 6.$
Answer$5 : 3 :: x : 6$
$\because\text{ad}=\text{bc}$
$\therefore5\times6=3\times\text{x}$
$\Rightarrow\text{x}=\frac{5\times6}{3}=10$
$\therefore\text{x}=10$
View full question & answer→Question 242 Marks
A car travels $195\ km$ in $3$ hours.How long will it take a travel $520\ km?$
AnswerThe car travel $195\ km$ in $3$ hours The car travel $1\ km$ in $\frac{3}{195}$ hours [less distance, less time]
The car travel $520\ km$ in $\frac{3}{195}\times520=8\text{ hour}$
Hence, the car travel $520\ km$ in $8$ hours.
View full question & answer→Question 252 Marks
The weight of $65$ books is $13\ kg$. How many such books weigh $6.4\ kg?$
Answer$13\ kg$ weight $= 65$ books $1\ kg$ weight $=\frac{65}{13}$ books [less weight, less book] $6.4\ kg$ weight $=\frac{65}{13}\times6.4=32\text{ books}$
Hence, $32$ books weigh $6.4\ kg.$
View full question & answer→Question 262 Marks
If $9\ kg$ of rice costs $Rs. 327.60$, what will be the cost of $50\ kg$ of rice?
AnswerCost of $9\ kg$ of rice $= Rs. 327.60$
Cost of $1\ kg$ of rice $\text{Rs }\Big(\frac{327.60}{9}\Big)$ [less rice, less cost]
cost of $50\ kg$ rice $=\text{Rs }\Big(\frac{32760}{9\times100}\times50\Big)=\text{Rs. }1820$
Hence, the cost of $50\ kg$ rice is $Rs. 1820.$
View full question & answer→Question 272 Marks
$35$ inland letters cost $Rs. 87.50.$ How many such letters can we buy for $315?$
AnswerFor $Rs. 87.50$ 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 $Rs. 315$
View full question & answer→Question 282 Marks
Verify the following: $108 : 72 :: 129 : 86$
AnswerWe have $108 : 72 :: 129 : 86$
Product of means $= 72 \times 129 = 9288$
Product of extremes $= 108 \times 86 = 9288$
Product of means = Product of extremes
Hence $108 : 72 :: 129 : 86$ is verified.
View full question & answer→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 $4$) $\therefore6:5$
View full question & answer→Question 302 Marks
Find the following ratios in the simplest form: $2.4\ km$ to $900m$
Answer$2.4\text{km to 900m}$
$=2400\text{m}:900\text{m}=\frac{2400}{900}$
$=\frac{2400\div300}{900\div300}$
$(\text{HCF of 2400 and 900 = 300})$
$=\frac{8}{3}=8:3$
View full question & answer→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 $300 = 12)$
$=\frac{7}{25}=7:25$
View full question & answer→Question 322 Marks
Verify the following: $60 : 105 :: 84: 147$
AnswerWe have $60 : 105 :: 84 : 147$
Product of means $= 105 \times 84 = 8820$
Product of extremes $= 60 \times 147 = 8820$
$\therefore$ Product of means = Product of extremes
Hence $60 : 105 :: 84 : 147$ is verified.
View full question & answer→Question 332 Marks
A labourer earns $Rs. 1980$ in $12$ days. How much does he earn in $7$ days?
AnswerIn $12$ 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.
View full question & answer→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 $24, 56 = 8$) $=\frac{3}{7}=3:7$
View full question & answer→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 $32 \times 210 = 48 \times 70$
If $6720 = 3360$
Which is not true
$\therefore 32, 48, 70, 210$ are not in proportion
View full question & answer→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 $28 \times 550$ 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.
View full question & answer→Question 372 Marks
If the cost of $14m$ of cloth is $Rs. 1890$, find the cost of $6m$ of cloth.
AnswerCost 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 $Rs. 810$
View full question & answer→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 $33 \times 96 = 121 \times 9$ If $3168 = 1089$
Which is not true $\therefore 33, 121,9, 96$ are not in proportion
View full question & answer→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 $(3 \times 60)$ 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.
View full question & answer→Question 402 Marks
If $12L $ of diesel is consumed by a car in covering a distance of $222\ km$, how many kilometres will it go in $22L $of diesel?
Answer$12L$ of diesel consumed by distance $= 222\ km$
$1L$ of diesel consumed by distance $=\frac{222}{12}\text{km}$
$22L$ diesel consumed by distance $=\frac{222}{12}\times22=407\text{km}$
Hence, $407\ km$ will the car go in $22L$ diesel.
View full question & answer→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?
AnswerIn $26$ days the work finished by $40$ men
In $1$ days the work finished by $40 \times 26$ 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.
View full question & answer→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 $5$)
$\therefore7:12$
View full question & answer→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 $7 \times 78 = 42 \times 13$
If $546 = 546$ Which is true
$\therefore 7, 42, 13, 78$ are in proportion.
View full question & answer→