Practice MCQ Questions and Answer on Chain Rule

21.

A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day than was planned, they could complete the job a day ahead of schedule. How many days did they take to complete the job ?

• (A) 8 days
• (B) 9 days
• (C) 10 days
• (D) 12 days

Show Answer

 Let the team take x days to finish 360 pieces Then, number of pieces made each day = $$\frac{{360}}{x}$$ More number of pieces per day, Less days (Indirect proportion) $$\eqalign{ & \therefore \,\left( {\frac{{360}}{x} + 4} \right):\frac{{360}}{x}::x:\left( {x - 1} \right) \cr & \Leftrightarrow \left( {\frac{{360}}{x} + 4} \right) \left( {x - 1} \right) = \frac{{360}}{x} \times x \cr & \Leftrightarrow 360 - \frac{{360}}{x} + 4x - 4 = 360 \cr & \Leftrightarrow 4x - \frac{{360}}{x} - 4 = 0 \cr & \Leftrightarrow x - \frac{{90}}{x} - 1 = 0 \cr & \Leftrightarrow {x^2} - x - 90 = 0 \cr & \Leftrightarrow \left( {x - 10} \right)\left( {x + 9} \right) = 0 \cr & \Leftrightarrow x = 10 \cr} $$

22.

Working 8 hours a day, 12 men can do a work in 30 days. Working 4 hours a day, 18 men can do work in ?

• (A) 30 days
• (B) 40 days
• (C) 45 days
• (D) 50 days

Show Answer

 Let the required number of days be x Less working hours, More days (Indirect Proportion) More men, Less days (Indirect Proportion) \[\left. \begin{gathered} {\text{Working hours 4}}:8 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Men 18}}:12 \hfill \\ \end{gathered} \right\}::30:x\] $$\eqalign{ & \therefore {\text{ }}4 \times 18 \times x = 8 \times 12 \times 30 \cr & \Leftrightarrow x = \frac{{\left( {8 \times 12 \times 30} \right)}}{{\left( {4 \times 18} \right)}} \cr & \Leftrightarrow x = 40 \cr} $$

23.

If 17 labourers can dig a ditch 26 m long in 18 days, working 8 hours a day; how many more labourers should be engaged to dig a similar ditch 39 m long in 6 days, each labourer working 9 hours a day ?

• (A) 34
• (B) 51
• (C) 68
• (D) 85

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 Let the total number of men to be engaged be $$x$$ More length, More labourers (Direct proportion) Less days, More labourers (Indirect proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,{\text{Lentgh 26}}:39 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 6}}:18 \hfill \\ {\text{Hours per day }}9:8 \hfill \\ \end{gathered} \right\}::17:x\] $$\eqalign{ & \therefore {\text{ }}26 \times 6 \times 9 \times x = 39 \times 18 \times 8 \times 17 \cr & \Leftrightarrow x = \frac{{\left( {39 \times 18 \times 8 \times 17} \right)}}{{\left( {26 \times 6 \times 9} \right)}} \cr & \Leftrightarrow x = 68 \cr} $$ ∴ Number of more labourers = (68 -17) = 51

24.

An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth ?

• (A) 178
• (B) 195
• (C) 24
• (D) 488

Show Answer

 Let the required time be x seconds Then, More metres, More time (direct proportion) $$\eqalign{ & \therefore 0.128:25::1:x \cr & \Leftrightarrow x = \frac{{25}}{{0.128}} \cr & \Leftrightarrow x = \frac{{25 \times 1000}}{{128}} \cr & \Leftrightarrow x = 195.31 \cr} $$` ∴ Required time =195 seconds (approx)

25.

The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozens of such mangoes ?

• (A) Rs. 3000
• (B) Rs. 3500
• (C) Rs. 4000
• (D) Rs. 2500

Show Answer

 Let the required price be Rs. x More mangoes, More price (Direct proportion) $$\eqalign{ & \therefore 357:\left( {49 \times 12} \right)::1517.25:x \cr & \Leftrightarrow 357x = \left( {49 \times 12 \times 1517.25} \right) \cr & \Leftrightarrow x = \frac{{\left( {49 \times 12 \times 1517.25} \right)}}{{357}} \cr & \Leftrightarrow x = 2499 \cr} $$ Hence, the approximate price is Rs. 2500

26.

In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

• (A) 1
• (B) $$\frac{1}{{40}}$$
• (C) 40
• (D) 80

Show Answer

 Let the required number of days be x. Less cows, More days (Indirect Proportion) Less bags, Less days (Direct Proportion) \[\left. \begin{gathered} {\text{Cows}}\,\,\,\,\,1:40 \hfill \\ {\text{Bags}}\,\,\,\,\,40:1 \hfill \\ \end{gathered} \right\}::40:x\] $$\eqalign{ & \therefore 1 \times 40 \times x = 40 \times 1 \times 40 \cr & \Rightarrow x = 40 \cr} $$

27.

If 5 engines consume 6 metric tonnes of coal when each is running 9 hours a day, how many metric tonnes of coal will be needed for 8 engines, each running 10 hours a day, it begin given that 3 engines of the former type consume as much as 4 engines of the latter type ?

• (A) $${\text{3}}\frac{1}{8}$$
• (B) 8
• (C) $${\text{8}}\frac{8}{9}$$
• (D) $${\text{6}}\frac{{12}}{{25}}$$

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 Let the required quantity of coal be x metric tonnes More engines, More coal (Direct proportion) More hours per day, More coal (Direct proportion) More rate, More coal (Direct proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Engines 5}}:8 \hfill \\ {\text{Hours per day 9}}:10 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Rate }}\frac{1}{3}:\frac{1}{4} \hfill \\ \end{gathered} \right\}::6:x\] $$\eqalign{ & \therefore \,\,\left( {5 \times 9 \times \frac{1}{3} \times x} \right) = \left( {8 \times 10 \times \frac{1}{4} \times 6} \right) \cr & \Leftrightarrow 15x = 120 \cr & \Leftrightarrow x = 8 \cr} $$

28.

In a barrack of soldiers there was stock of food for 190 days for 4000 soldiers. After 30 days 800 soldiers left the barrack. For how many days shall the left over food last for the remaining soldiers ?

• (A) 175 days
• (B) 200 days
• (C) 225 days
• (D) 250 days

Show Answer

 Let the remaining food last for x days 4000 soldiers had provision for 160 days 3200 soldiers had provision for x days Less men, More days (Indirect proportion) $$\eqalign{ & \therefore \,3200:4000::160:x \cr & \Leftrightarrow 3200x = 4000 \times 160 \cr & \Leftrightarrow x = \frac{{\left( {4000 \times 160} \right)}}{{3200}} \cr & \Leftrightarrow x = 200 \cr} $$

29.

The cost of 5 kgs of apples is Rs. 450. The cost of 12 dozen mangoes is Rs. 4320 and the cost of 4 kgs of oranges is Rs. 240. What is the total cost of 8 kg of apples, 8 dozen of mangoes and 8 kg of oranges ?

• (A) Rs. 4020
• (B) Rs. 4080
• (C) Rs. 4050
• (D) Other than those given as option

Show Answer

 Cost of 5 kgs apples Rs. 450 Cost of 1 kg apples Rs. $$\frac{{{\text{450}}}}{5}$$ Cost of 8 kgs apples = $$\frac{{450}}{5} \times 8$$   = Rs.720 Cost of 12 dozens mangoes Rs. 4320 Cost of 1 dozen mangoes Rs. $$\frac{{{\text{4320}}}}{{12}}$$ Cost of 8 dozen mangoes = $$\frac{{4320}}{{12}} \times 8$$   = Rs. 2880 Cost of 4 kgs oranges = Rs. 240 Cost of 1 kg orange = Rs. $$\frac{{{\text{240}}}}{4}$$ Cost of 8 kgs oranges = $$\frac{{240}}{4} \times 8$$   = Rs. 480 Total cost = 720 + 2880 + 480 = Rs. 4080

30.

50 people consume 350 kg of rice in 30 days. In how many days will 35 people consume 50 kg of rice ?

• (A) 2 days
• (B) 3 days
• (C) 5 days
• (D) 7 days

Show Answer

Answer & Solution Answer: Option E Solution: Let the required number of days be x Less people, More days (Indirect proportion) Less quantity, Less days ( Direct proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,{\text{People 35}}:50 \hfill \\ {\text{Quantity 350}}:50 \hfill \\ \end{gathered} \right\}::30:x\] $$\eqalign{ & \therefore {\text{ }}35 \times 350 \times x = 50 \times 50 \times 30 \cr & \Leftrightarrow x = \frac{{\left( {50 \times 50 \times 30} \right)}}{{\left( {35 \times 350} \right)}} \cr & \Leftrightarrow x = \frac{{300}}{{49}} \cr & \Leftrightarrow x = 6\frac{6}{{49}} \cr} $$