Class 8: Decimals – Exercise 6C

$\displaystyle \textbf{Question 1: }\text{Express using decimals:}$
$\displaystyle \text{(i) }408\text{ paise in rupees}\qquad\text{(ii) }17\text{ rupees }86\text{ paise in rupees}$
$\displaystyle \text{(iii) }673\text{ mm in metres}\qquad\text{(iv) }72\text{ cm in kilometres}$
$\displaystyle \text{(v) }481\text{ mg in grams}\qquad\text{(vi) }92\text{ kg }45\text{ g in kilograms}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{(i) Since }100\text{ paise}=1\text{ rupee},$
$\displaystyle 408\text{ paise}=\frac{408}{100}\text{ rupees}=4.08\text{ rupees}.$

$\displaystyle \text{(ii) }17\text{ rupees }86\text{ paise} =17+\frac{86}{100}\text{ rupees}$
$\displaystyle =17+0.86=17.86\text{ rupees}.$

$\displaystyle \text{(iii) Since }1000\text{ mm}=1\text{ metre},$
$\displaystyle 673\text{ mm}=\frac{673}{1000}\text{ metres}=0.673\text{ metres}.$

$\displaystyle \text{(iv) Since }100000\text{ cm}=1\text{ kilometre},$
$\displaystyle 72\text{ cm}=\frac{72}{100000}\text{ kilometres}=0.00072\text{ kilometres}.$

$\displaystyle \text{(v) Since }1000\text{ mg}=1\text{ gram},$
$\displaystyle 481\text{ mg}=\frac{481}{1000}\text{ grams}=0.481\text{ grams}.$

$\displaystyle \text{(vi) Since }1000\text{ g}=1\text{ kg},$
$\displaystyle 92\text{ kg }45\text{ g} =92+\frac{45}{1000}\text{ kg}=92.045\text{ kg}.$
$\displaystyle \\$

$\displaystyle \textbf{Question 2: }\text{Aditya travelled }28.96\text{ km by car while}$
$\displaystyle \text{Sriraj travelled }91.48\text{ km. Who travelled more and by how much?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Since }91.48>28.96,\text{ Sriraj travelled more.}$
$\displaystyle \text{Difference}=91.48-28.96=62.52\text{ km}.$
$\displaystyle \therefore \text{Sriraj travelled }62.52\text{ km more than Aditya.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 3: }\text{A trader bought a notebook for Rs. }27.50,\text{ a book}$
$\displaystyle \text{for Rs. }198.43\text{ and a pen for Rs. }145.65.\text{ He sold all the three}$
$\displaystyle \text{things for Rs. }375.\text{ Find his profit or loss.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Total Cost Price}=27.50+198.43+145.65=\text{Rs. }371.58.$
$\displaystyle \text{Total Selling Price}=\text{Rs. }375.$
$\displaystyle \text{Since Selling Price}>\text{Cost Price, there is a profit.}$
$\displaystyle \text{Profit}=375-371.58=\text{Rs. }3.42.$
$\displaystyle \therefore \text{The trader made a profit of Rs. }3.42.$
$\displaystyle \\$

$\displaystyle \textbf{Question 4: }\text{By how much should }491.18\text{ be decreased to get }209.76\text{?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the required number be }x.$
$\displaystyle 491.18-x=209.76$
$\displaystyle x=491.18-209.76=281.42.$
$\displaystyle \therefore 491.18\text{ should be decreased by }281.42.$
$\displaystyle \\$

$\displaystyle \textbf{Question 5: }\text{The cost of one electric oven is Rs. }75.\text{ Find the cost}$
$\displaystyle \text{of }47\text{ such electric ovens.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Cost of one electric oven}=\text{Rs. }75.$
$\displaystyle \text{Cost of }47\text{ electric ovens}=75\times47=\text{Rs. }3525.$
$\displaystyle \therefore \text{The cost of }47\text{ electric ovens is Rs. }3525.$
$\displaystyle \\$

$\displaystyle \textbf{Question 6: }\text{One gram of gold costs Rs. }40.\text{ How much does a}$
$\displaystyle \text{bracelet made of }48.28\text{ g of gold cost?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Cost of }1\text{ g of gold}=\text{Rs. }40.$
$\displaystyle \text{Cost of }48.28\text{ g of gold}=40\times48.28=\text{Rs. }1931.20.$
$\displaystyle \therefore \text{The bracelet costs Rs. }1931.20.$
$\displaystyle \\$

$\displaystyle \textbf{Question 7: }\text{A car covers }9.7\text{ km on one litre of petrol. How much}$
$\displaystyle \text{distance will it cover in }52.56\text{ litres of petrol?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Distance covered in }1\text{ litre of petrol}=9.7\text{ km}.$
$\displaystyle \text{Distance covered in }52.56\text{ litres}=9.7\times52.56\text{ km}.$
$\displaystyle =509.832\text{ km}.$
$\displaystyle \therefore \text{The car will cover }509.832\text{ km}.$
$\displaystyle \\$

$\displaystyle \textbf{Question 8: }\text{Find the average of the numbers }17.56,\ 22.43,\ 91.35$
$\displaystyle \text{and }48.3.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Average}=\frac{17.56+22.43+91.35+48.3}{4}$
$\displaystyle =\frac{179.64}{4}=44.91.$
$\displaystyle \therefore \text{The average is }44.91.$
$\displaystyle \\$

$\displaystyle \textbf{Question 9: }\text{The perimeter of a polygon is }25.34\text{ cm. If the length}$
$\displaystyle \text{of each side is }3.62\text{ cm, find the number of sides of the polygon.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Number of sides}=\frac{\text{Perimeter}}{\text{Length of each side}}$
$\displaystyle =\frac{25.34}{3.62}=7.$
$\displaystyle \therefore \text{The polygon has }7\text{ sides.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 10: }\text{How many pieces of plywood, each }0.55\text{ cm thick, are}$
$\displaystyle \text{required to make a pile }2.53\text{ m high?}$
$\displaystyle \text{Answer:}$
$\displaystyle 2.53\text{ m}=2.53\times100=253\text{ cm}.$
$\displaystyle \text{Number of pieces}=\frac{253}{0.55}=460.$
$\displaystyle \therefore 460\text{ pieces of plywood are required.}$
$\displaystyle \\$

$\displaystyle \textbf{Question 11: }\text{A sum of Rs. }6512\text{ was divided among }100\text{ boys}$
$\displaystyle \text{and girls such that each boy gets Rs. }73.60\text{ and each girl gets}$
$\displaystyle \text{Rs. }52.40.\text{ Find the number of girls.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the number of girls be }x.$
$\displaystyle \therefore \text{Number of boys}=100-x.$
$\displaystyle 52.40x+73.60(100-x)=6512$
$\displaystyle 52.40x+7360-73.60x=6512$
$\displaystyle 21.20x=848$
$\displaystyle x=\frac{848}{21.20}=40.$
$\displaystyle \therefore \text{The number of girls is }40.$
$\displaystyle \\$

$\displaystyle \textbf{Question 12: }\text{An employee may claim Rs. }12.50\text{ for each km}$
$\displaystyle \text{he travels by taxi and Rs. }9.25\text{ for each km he drives his own car.}$
$\displaystyle \text{If on a particular day he claimed Rs. }779\text{ for travelling a distance of}$
$\displaystyle 80\text{ km, how many km did he drive his own car?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the distance travelled by his own car be }x\text{ km}.$
$\displaystyle \therefore \text{Distance travelled by taxi}=(80-x)\text{ km}.$
$\displaystyle 12.50(80-x)+9.25x=779$
$\displaystyle 1000-12.50x+9.25x=779$
$\displaystyle 1000-3.25x=779$
$\displaystyle 3.25x=221$
$\displaystyle x=\frac{221}{3.25}=68.$
$\displaystyle \therefore \text{He drove }68\text{ km in his own car.}$
$\displaystyle \\$