\displaystyle \textbf{Question 1: }\text{If the cost of }40\text{ toys is Rs. }1024, \text{ what is the cost of}
\displaystyle \text{one dozen such toys?}
\displaystyle \text{Answer:}
\displaystyle \text{Cost of }40\text{ toys}=\text{Rs. }1024.
\displaystyle \text{Cost of }1\text{ toy}=\text{Rs. }\frac{1024}{40} =\text{Rs. }25.60.
\displaystyle \text{One dozen toys}=12\text{ toys}.
\displaystyle \text{Cost of }12\text{ toys}=\text{Rs. }25.60\times12 =\text{Rs. }307.20.
\displaystyle \therefore \text{the cost of one dozen toys is Rs. }307.20.
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{If }18\text{ notebooks cost Rs. }333, \text{ how many notebooks can be purchased}
\displaystyle \text{for Rs. }425.50?
\displaystyle \text{Answer:}
\displaystyle \text{Cost of }18\text{ notebooks}=\text{Rs. }333.
\displaystyle \text{Cost of }1\text{ notebook} =\text{Rs. }\frac{333}{18}=\text{Rs. }18.50.
\displaystyle \text{Number of notebooks that can be purchased for Rs. }425.50
\displaystyle =\frac{425.50}{18.50}=23.
\displaystyle \therefore 23\text{ notebooks can be purchased for Rs. }425.50.
\displaystyle \\

\displaystyle \textbf{Question 3: }\text{If }50\text{ pencils can be bought for Rs. }120, \text{ how many pencils can be bought}
\displaystyle \text{for Rs. }108?
\displaystyle \text{Answer:}
\displaystyle \text{Cost of }50\text{ pencils}=\text{Rs. }120.
\displaystyle \text{Cost of }1\text{ pencil}=\text{Rs. }\frac{120}{50} =\text{Rs. }2.40.
\displaystyle \text{Number of pencils that can be bought for Rs. }108 =\frac{108}{2.40}=45.
\displaystyle \therefore 45\text{ pencils can be bought for Rs. }108.
\displaystyle \\

\displaystyle \textbf{Question 4: }\text{If }45\text{ iron rods of the same size weigh }12.6\text{ kg,}
\displaystyle \text{how much do }24\text{ such rods weigh?}
\displaystyle \text{Answer:}
\displaystyle \text{Weight of }45\text{ rods}=12.6\text{ kg}.
\displaystyle \text{Weight of }1\text{ rod}=\frac{12.6}{45}=0.28\text{ kg}.
\displaystyle \text{Weight of }24\text{ rods}=0.28\times24=6.72\text{ kg}.
\displaystyle \therefore \text{the weight of }24\text{ rods is }6.72\text{ kg}.
\displaystyle \\

\displaystyle \textbf{Question 5: }\text{If a labourer earns Rs. }784\text{ per week, how much}
\displaystyle \text{will he earn in }15\text{ days?}
\displaystyle \text{Answer:}
\displaystyle \text{Earnings for }7\text{ days}=\text{Rs. }784.
\displaystyle \text{Earnings for }1\text{ day} =\text{Rs. }\frac{784}{7}=\text{Rs. }112.
\displaystyle \text{Earnings for }15\text{ days} =\text{Rs. }112\times15=\text{Rs. }1680.
\displaystyle \therefore \text{The labourer will earn Rs. }1680\text{ in }15\text{ days}.
\displaystyle \\

\displaystyle \textbf{Question 6: }\text{If a car covers }56.7\text{ km in }4.5\text{ litres of petrol,}
\displaystyle \text{how many kilometres will it cover in }26\text{ litres of petrol?}
\displaystyle \text{Answer:}
\displaystyle \text{Distance covered using }4.5\text{ litres of petrol}=56.7\text{ km}.
\displaystyle \text{Distance covered using }1\text{ litre of petrol} =\frac{56.7}{4.5}=12.6\text{ km}.
\displaystyle \text{Distance covered using }26\text{ litres of petrol} =12.6\times26=327.6\text{ km}.
\displaystyle \therefore \text{the car will cover }327.6\text{ km}.
\displaystyle \\

\displaystyle \textbf{Question 7: }15\text{ men can do a piece of work in }36\text{ hours.}
\displaystyle \text{How many men will be required to finish the work in }20\text{ hours?}
\displaystyle \text{Answer:}
\displaystyle 15\text{ men can complete the work in }36\text{ hours}.
\displaystyle \text{Total work}=15\times36=540\text{ man-hours}.
\displaystyle \text{Number of men required to complete the work in }20\text{ hours}
\displaystyle =\frac{540}{20}=27.
\displaystyle \therefore 27\text{ men will be required to finish the work in }20\text{ hours}.
\displaystyle \\

\displaystyle \textbf{Question 8: }13\text{ men can weave }117\text{ baskets in a week.}
\displaystyle \text{How many men will be needed to weave }189\text{ baskets in }3\text{ days?}
\displaystyle \text{Answer:}
\displaystyle 13\text{ men working for }7\text{ days} =13\times7=91\text{ man-days}.
\displaystyle 117\text{ baskets require }91\text{ man-days}.
\displaystyle 1\text{ basket requires } \frac{91}{117}=\frac{7}{9}\text{ man-day}.
\displaystyle 189\text{ baskets require } 189\times\frac{7}{9}=147\text{ man-days}.
\displaystyle \text{Number of men required to complete the work in }3\text{ days}
\displaystyle =\frac{147}{3}=49.
\displaystyle \therefore 49\text{ men will be needed to weave }189\text{ baskets in }3\text{ days}.
\displaystyle \\

\displaystyle \textbf{Question 9: }\text{A journey by car takes }48\text{ minutes at }65\text{ km/hr.}
\displaystyle \text{How fast must the car go to finish the journey in }40\text{ minutes?}
\displaystyle \text{Answer:}
\displaystyle \text{Distance covered in }48\text{ minutes} =65\times\frac{48}{60}=52\text{ km}.
\displaystyle \text{Time available}=40\text{ minutes} =\frac{40}{60}\text{ hour}.
\displaystyle \text{Required speed} =\frac{52}{40/60}=\frac{52\times60}{40}=78\text{ km/hr}.
\displaystyle \therefore \text{the car must travel at }78\text{ km/hr}.
\displaystyle \\

\displaystyle \textbf{Question 10: }\text{In a zoo, }28\text{ parrots consume }7420\text{ g of nuts in a day.}
\displaystyle \text{If }8\text{ parrots are sent to another zoo, what quantity of nuts will be}
\displaystyle \text{required in a day?}
\displaystyle \text{Answer:}
\displaystyle 28\text{ parrots consume }7420\text{ g of nuts per day}.
\displaystyle 1\text{ parrot consumes }\frac{7420}{28}=265\text{ g of nuts per day}.
\displaystyle \text{Number of parrots remaining}=28-8=20.
\displaystyle 20\text{ parrots consume }265\times20=5300\text{ g of nuts per day}.
\displaystyle \therefore 5300\text{ g of nuts will be required per day}.
\displaystyle \\

\displaystyle \textbf{Question 11: }\text{If }5\text{ men or }7\text{ women can earn Rs. }700\text{ per day,}
\displaystyle \text{how much would }7\text{ men and }11\text{ women earn per day?}
\displaystyle \text{Answer:}
\displaystyle 5\text{ men earn Rs. }700\text{ per day}.
\displaystyle 1\text{ man earns Rs. }\frac{700}{5}=\text{Rs. }140\text{ per day}.
\displaystyle 7\text{ women earn Rs. }700\text{ per day}.
\displaystyle 1\text{ woman earns Rs. }\frac{700}{7}=\text{Rs. }100\text{ per day}.
\displaystyle \text{Earnings of }7\text{ men}=7\times140=\text{Rs. }980.
\displaystyle \text{Earnings of }11\text{ women}=11\times100=\text{Rs. }1100.
\displaystyle \text{Total earnings}=980+1100=\text{Rs. }2080\text{ per day}.
\displaystyle \therefore 7\text{ men and }11\text{ women would earn Rs. }2080\text{ per day}.
\displaystyle \\

\displaystyle \textbf{Question 12: }\text{If }5\text{ labourers earn Rs. }9000\text{ in }15\text{ days,}
\displaystyle \text{how many labourers can earn Rs. }6720\text{ in }8\text{ days?}
\displaystyle \text{Answer:}
\displaystyle 5\text{ labourers working for }15\text{ days} =5\times15=75\text{ labourer-days}.
\displaystyle 75\text{ labourer-days earn Rs. }9000.
\displaystyle 1\text{ labourer-day earns Rs. } \frac{9000}{75}=\text{Rs. }120.
\displaystyle \text{Labourer-days required to earn Rs. }6720 =\frac{6720}{120}=56.
\displaystyle \text{Number of labourers required for }8\text{ days} =\frac{56}{8}=7.
\displaystyle \therefore 7\text{ labourers can earn Rs. }6720\text{ in }8\text{ days}.
\displaystyle \\

\displaystyle \textbf{Question 13: }\text{A fort had provisions for }450\text{ men for }80\text{ days.}
\displaystyle \text{After }10\text{ days, }50\text{ more men arrived. How long will the remaining}
\displaystyle \text{food last at the same rate?}
\displaystyle \text{Answer:}
\displaystyle \text{Total provisions}=450\times80=36000\text{ man-days}.
\displaystyle \text{Food consumed by }450\text{ men in }10\text{ days} =450\times10=4500\text{ man-days}.
\displaystyle \text{Provisions remaining}=36000-4500=31500\text{ man-days}.
\displaystyle \text{Number of men after }10\text{ days}=450+50=500.
\displaystyle \text{Number of days the remaining provisions will last} =\frac{31500}{500}=63.
\displaystyle \therefore \text{the remaining food will last for }63\text{ days}.
\displaystyle \\

\displaystyle \textbf{Question 14: }3\text{ typists working }7\text{ hours a day can type a thesis}
\displaystyle \text{in }10\text{ days. For how many hours per day should }2\text{ typists work}
\displaystyle \text{to finish it in }21\text{ days?}
\displaystyle \text{Answer:}
\displaystyle \text{Total work}=3\times7\times10=210\text{ typist-hours}.
\displaystyle \text{Let the required number of working hours per day be }x.
\displaystyle 2\times21\times x=210.
\displaystyle 42x=210.
\displaystyle x=\frac{210}{42}=5.
\displaystyle \therefore 2\text{ typists should work }5\text{ hours per day}.
\displaystyle \\

\displaystyle \textbf{Question 15: }7\text{ workers working }6\text{ hours a day can build a wall}
\displaystyle \text{in }12\text{ days. How many days will }3\text{ workers take to build a similar}
\displaystyle \text{wall, working }8\text{ hours a day?}
\displaystyle \text{Answer:}
\displaystyle \text{Total work}=7\times6\times12=504\text{ worker-hours}.
\displaystyle \text{Let the required number of days be }x.
\displaystyle 3\times8\times x=504.
\displaystyle 24x=504.
\displaystyle x=\frac{504}{24}=21.
\displaystyle \therefore 3\text{ workers will take }21\text{ days to build the wall}.
\displaystyle \\

Discover more from ICSE / ISC / CBSE Mathematics Portal for K12 Students

Subscribe to get the latest posts sent to your email.