Practice MCQ Questions and Answer on Chain Rule

31.

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

Show Answer

 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

32.

If 2 m, 60 cm cloths is required for one shirt, then the cloth required for 7 shirts is ?

• (A) 14 m 80 cm
• (B) 18 m 20 cm
• (C) 15 m 20 cm
• (D) 16 m 80 cm

Show Answer

 Cloth is required for 1 shirt = 2 m, 60 cm or 260 cm Cloth is required for 7 shirt = 260 × 7 = 1820 cm or 18 m 20 cm

33.

2 persons working 2 hours a day assemble 2 machine in 2 days. The number of machines assemble by 6 persons working 6 hours a day in 6 day is ?

• (A) 6
• (B) 18
• (C) 27
• (D) 54

Show Answer

 Let the required number of machine be x More persons, More machines (Direct proportion) More working working hours, More machines (Direct proportion) More days, More machines (Direct proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Persons 2}}:6 \hfill \\ \,\,\,\, {\text{Working hours 2}}:6 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 2}}:{\text{6}} \hfill \\ \end{gathered} \right\}::2:x\] $$\eqalign{ & \therefore {\text{ }}2 \times 2 \times 2 \times x = 6 \times 6 \times 6 \times 2 \cr & \Leftrightarrow x = \frac{{\left( {6 \times 6 \times 6 \times 2} \right)}}{{\left( {2 \times 2 \times 2} \right)}} \cr & \Leftrightarrow x = 54 \cr} $$

34.

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

• (A) $$29\frac{1}{5}$$
• (B) $$37\frac{1}{4}$$
• (C) 42
• (D) 54

Show Answer

 After 10 days : 150 men had food for 35 days. Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion) $$\eqalign{ & \therefore 125:150::35:x \cr & \Rightarrow 125 \times x = 150 \times 35 \cr & \Rightarrow x = \frac{{150 \times 35}}{{125}} \cr & \Rightarrow x = 42 \cr} $$

35.

The work done by a women in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same work, working 8 hours per day ?

• (A) $$\text{1}\frac{1}{2}\text{ days}$$
• (B) $$\text{3 days}$$
• (C) $$\text{3}\frac{2}{3}\text{ days}$$
• (D) $$\text{4}\frac{1}{2}\text{ days}$$

Show Answer

 Ratio of time taken by a woman, a man and a boy $$\eqalign{ & = 8:6:12 \cr & = 4:3:6 \cr} $$ So, 4 women ≡ 3 men ≡ 6 boy (12 mens + 12 womens + 12 boys) $$\eqalign{ & = \left[ {12 + \left( {\frac{3}{4} \times 12} \right) + \left( {\frac{3}{6} \times 12} \right)} \right]{\text{men}} \cr & {\text{ = }}\left( {12 + 9 + 6} \right){\text{men}} \cr & = 27{\text{ men}} \cr} $$ Let the required number of days be x More men, Less days (Indirect proportion) More working hours, Less days (Indirect proportion) \[\left. \begin{gathered} {\text{Working hours 8}}:6 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Men 27}}:9 \hfill \\ \end{gathered} \right\}::6:x\] $$\eqalign{ & \therefore \,27 \times 8 \times x = 9 \times 6 \times 6 \cr & \Leftrightarrow x = \frac{{\left( {9 \times 6 \times 6} \right)}}{{\left( {27 \times 8} \right)}} \cr & \Leftrightarrow x = \frac{3}{2} \cr & \Leftrightarrow x = 1\frac{1}{2} \cr} $$

36.

12 persons can do a piece of work in 4 days. How many persons are required to complete 8 times the work in half the time ?

• (A) 144
• (B) 180
• (C) 190
• (D) 192

Show Answer

 Let the required number of persons be x Less days , More persons (Indirect proportion) More work , More persons (Direct proportion) \[\left. \begin{gathered} \,{\text{Days 2}}:4 \hfill \\ {\text{Work 1}}:8 \hfill \\ \end{gathered} \right\}::12:x\] $$\eqalign{ & \therefore \,2 \times 1 \times x = 4 \times 8 \times 12 \cr & \Leftrightarrow x = \frac{{\left( {4 \times 8 \times 12} \right)}}{{\left( 2 \right)}} \cr & \Leftrightarrow x = 192 \cr} $$

37.

12 men and 18 boys, working $$7\frac{1}{2}$$ hours a day, can do a piece of work in 60 days. If a man works equal to 2 boys, then how many boys will be required to help 21 men to do twice the work in 50 days, working 9 hours a day ?

• (A) 30
• (B) 42
• (C) 48
• (D) 90

Show Answer

 1 man ≡ 2 boys ⇔ (12 men + 18 boys)           ≡ (12 × 2 ×18) boys = 42 boys Let required number of boys = x ⇒ (21 men + x boys) ≡ (21 × 2 × x) boys = (42 + x) boys Less days, More boys (Indirect proportion) More hours per day, Less boys (Indirect proportion) More work, More boys (Direct proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 50}}:60 \hfill \\ {\text{Hours per day 9}}:\frac{{15}}{2} \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Work }}1:2 \hfill \\ \end{gathered} \right\}::42:\left( {42 + x} \right)\] $$\therefore \left[ {50 \times 9 \times 1 \times \left( {42 + x} \right)} \right] = $$     $$\left( {60 \times \frac{{15}}{2} \times 2 \times 42} \right)$$ $$\eqalign{ & \Leftrightarrow \left( {42 + x} \right) = \frac{{37800}}{{450}} \cr & \Leftrightarrow 42 + x = 84 \cr & \Leftrightarrow x = 42 \cr} $$

38.

The cost of 21 pencils and 9 clippers is Rs. 819. The cost price of 7 pencils and 3 clippers is = ?

• (A) Rs. 204
• (B) Rs. 409
• (C) Rs. 273
• (D) Rs. 208

Show Answer

 Cost of 21 pencils and 9 clippers = Rs. 819 Cost of 7 pencils and 3 clippers = $$\frac{{819}}{3}$$ = Rs. 273

39.

Four gardeners with four grass mowers mow 400 sq. m of ground in 4 hours. How long would it take for eight gardeners with eight grass mowers to mow 800 sq. m of ground ?

• (A) 4 hours
• (B) 6 hours
• (C) 8 hours
• (D) 12 hours

Show Answer

 Since each gardener would work with one grass mower, So, we shall consider 1 gardener and 1 grass mower as one unit. Let the required time be x hours More gardeners and grass mowers, Less time (Indirect proportion) More area, More time (Direct proportion) \[\left. \begin{gathered} {\text{Gardeners & grass mowers 8}}:4 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Area 400}}:800 \hfill \\ \end{gathered} \right\}::4:x\] $$\eqalign{ & \therefore {\text{ }}8 \times 400 \times x = 4 \times 800 \times 4 \cr & \Leftrightarrow x = \frac{{\left( {4 \times 800 \times 4} \right)}}{{\left( {8 \times 400} \right)}} \cr & \Leftrightarrow x = 4 \cr} $$

40.

A canteen requires 651 bananas for a week. Totally, how many bananas will it require for the months of April, May and June ?

• (A) 8463
• (B) 8547
• (C) 9086
• (D) 9284

Show Answer

 Total number of days = (30 + 31 + 30) = 91 Let the number of bananas be x More days, More bananas (Direct proportion) $$\eqalign{ & \therefore 7:91::651:x \cr & \Rightarrow 7x = 91 \times 651 \cr & \Rightarrow x = \left( {\frac{{91 \times 651}}{7}} \right) \cr & \Rightarrow x = 8463 \cr} $$