Class 6 Ratio, Proportion and Unitary Method Exercise 9.4

\begin{array}{l} \text {Q1. The price of 3 metres of cloth is Rs 79.50. } \\ \text {Find the price of 15 metres of such cloth. } \\ \\\text {Sol. Given that price of 3 metres of cloth is Rs. 79.50} \\ \therefore \text {Price of 1 metre of cloth} = \text {Rs. } \frac {79.50}{3} \\\text {Hence, the price of 15 metres of cloth } = \text {Rs. } \frac {79.50}{3} \times 15 =\text {Rs. } 397.50 \\ \\\text {Q2. The cost of 17 chairs is Rs. 9605.} \\ \text {Find the number of chairs that can be purchased in Rs. 56500.} \\ \\\text {Sol. Given that cost of 17 chairs is Rs. 9605} \\ \therefore \text {Cost of 1 chair} = \text {Rs. } \frac {9605}{17} = \text {Rs. } 565 \\\text {Hence, the number of chairs purchased in Rs. 56500 } = \frac {56500}{565} = 100 \text { chairs} \\ \\\text {Q3. Three ferryloads are needed to carry 150 people across a river. } \\ \text {How many people will be carried on 4 ferryloads? } \\ \\\text {Sol. Given that 3 ferryloads are need to carry 150 people.} \\ \therefore \text {1 ferryloads can carry } = \frac {150}{3} = 50 \text { people} \\\text {Hence, 4 ferryloads can carry } = 4 \times 50 = 200 \text { people} \\ \\ \\\text {Q4. If 9 kg of rice costs Rs. 120.60, what will 50 kg of such a quality of rice cost? } \\ \\\text {Sol. Given that 9 kg of rice costs Rs. 120.60} \\ \therefore \text {Cos of 1 kg of rice } = \text {Rs. } \frac {120.60}{9} \\\text {Hence, cost of 50 kg of rice } = \frac {120.60}{9} \times 50 = \text {Rs. } 670 \\ \\\text {Q5. A train runs 200 kilometres in 5 hours.} \\ \text {How many kilometres does it run in 7 hours? } \\ \\\text {Sol. Given that distance travel by train in 5 hrs } = 200 \text { km} \\ \therefore \text {Distance travel by train in 1 hr } = \frac {200}{5} = 40 \text { km} \\\text {Hence, distance travel by train in 7 hrs } = 40 \times 7 = 280 \text { km} \\ \\\text {Q6. 10 boys can dig a pitch in 12 hours.} \\ \text {How long will 8 boys take to do it? } \\ \\\text {Sol. Given that 10 boys can dig a pitch in 12 hours. } \\ \therefore \text {Time taken by 1 boy to dig the pitch or total effort required to dig the pitch} \\ = 10 \times 12 = 120 \text { hrs} \\\text {Hence, Time taken by 8 boys to dig the pitch } = \frac {120}{8} = 15 \text { hrs} \\ \\\text {Q7. A man can work 8 hours daily and finishes a work in 12 days. } \\ \text {If he works 6 hrs daily, in how many days will the same work be finished? } \\ \\\text {Sol. Given that one man can work 8 hours daily and finishes a work in 12 days } \\ \Rightarrow \text {Total time required to finish the work} = 8 \times 12 = 96 \text { hrs} \\\therefore \text {No. of days required to finish the work, working 6 hrs a day} \\= \frac {96}{6} = 16 \text { days} \\\text {Hence, the man need 16 days to finish the work by working 6 hrs daily.} \\ \\\text {Q8. Fifteen post cards cost Rs 2.25. What will be the cost of 36 post cards? } \\ \text {How many postcards can we buy in Rs 45 ? } \\ \\\text {Sol. Given that cost of 15 postcards is Rs. 2.25} \\ \therefore \text {Cost of 1 postcard} = \text {Rs. } \frac {2.25}{15} \\ \Rightarrow \text {Cost of 36 postcards } = \text {Rs. } \frac {2.25}{15} \times 36 = \text {Rs. } 5.40 \\\text {No. of post card we can buy in Rs. 45 } \\ = \frac {45}{\text {Cost of 1 post card}} \\ =\frac {45 \times 15}{2.25} \\ =300 \\ \\\text {Q9. A rail journey of 75 km costs Rs 215.} \\ \text {How much will a journey of 120 km cost? } \\ \\\text {Sol. Given that cost of 75 km journey is Rs. 215} \\ \therefore \text {Cost of 1 km journey} = \text {Rs. } \frac {215}{75} \\ \text {Hence, the cost of journey of 120 km } = \text {Rs. } \frac {215}{75} \times 120 = \text {Rs. } 344 \\ \\\text {Q10. If the sales tax on a purchase worth Rs. 60 is Rs. 4.20. } \\ \text {What will be the sales tax on the purchase worth Rs. 150 ? } \\ \\\text {Sol. Given that sales tax on a purchase worth Rs. 60 is Rs. 4.20} \\ \therefore \text {Sales tax on purchase of 1 Rs.} = \text {Rs. } \frac {4.20}{60} \\\text {Hence, Sales tax on purchase of 150 Rs.} = \text {Rs. } \frac {4.20}{60} \times 150 = \text {Rs. } 10.50 \\ \\\text {Q11. The cost of 17 chairs is Rs. 19210. Find the number of such chairs } \\ \text {that can be purchased in Rs. 113000 ? } \\ \\\text {Sol. Given that cost of 17 chairs is Rs. 19210} \\ \therefore \text {Cost of 1 chair} = \text {Rs. } \frac {19210}{17} \text {Rs. } 1130 \\\text {Hence, the number of chairs purchased in Rs. 113000 } = \frac {113000}{1130} = 100 \text { chairs} \\ \\\text {Q12. A car travels 165 km in 3 hours.} \\ \text {(i) How long will it take to travel 440 km ? } \\ \text {(ii) How far will it travel in 7 hours? } \\ \\\text {Sol. Given that distance travel by car in 3 hrs } = 165 \text { km} \\ \therefore \text {Distance travel by car in 1 hr } = \frac {165}{3} = 55 \text { km} \\\text {(i) Time taken by car to travel 440 kms } = \frac {440}{55} = 8 \text { hrs} \\ \\ \text {(ii) Distance travel by car in 7 hrs } = 55 \times 7 = 385 \text { km} \\ \\\text {Q13. 2 dozens of oranges cost Rs. 60. Find the cost of 120 similar oranges? } \\ \\\text {Sol. Given that 2 dozens of oranges cost Rs. 60.} \\ \Rightarrow \text {Cost of 24 oranges }= \text {Rs. } 60 \\ \Rightarrow \text {Cost of 1 orange }= \text {Rs. } \frac {60}{24} \\ \Rightarrow \text {Cost of 120 oranges }= \text {Rs. } \frac {60}{24} \times 120 = \text {Rs. } 300 \\ \\\text {Q14. A family of 4 members consumes 6 kg of sugar in a month. } \\ \text {What will be the monthly consumption of sugar, } \\ \text {if the number of family members becomes 6 ? } \\ \\\text {Sol. Given that 4 members consumes 6 kg of sugar in a month.} \\ \Rightarrow \text {Amount of sugar consumed by 1 member in the month }= \frac {6}{4} \text { kg} \\ \Rightarrow \text {Amount of sugar consumed by 6 member in the month }= \frac {6}{4} \times 6 = 9 \text { kg} \\\text {Q15. The weight of 45 folding chairs is 18 kg. How many such chairs } \\ \text {can be loaded on a truck having a capacity of carrying 4000 kg load? } \\ \\\text {Sol. Given that weight of 45 folding chairs is 18 kg.} \\ \therefore \text {Weight of 1 folding chair} = \frac {18}{45} \text { kg} \\\text {Hence, max. chairs that can be loading in a truck having capacity of 4000 kg} \\ = \frac {4000}{\frac {18}{45}} \\ = \frac {4000 \times 45}{18} \\ = 10000 \text { chairs} \\ \\\end{array}