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31. If 5 workers can collect 60 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days ?

A. 80 kg

B. 100 kg

C. 120 kg

D. 160 kg

Discuss

Solution:

Let the required quantity be x kg.
More workers, More quantity (Direct proportion)
More days, More quantity (Direct proportion)

\begin{matrix} Workers 5 : 8 \\ Days 3 : 5 \end{matrix}} :: 60 : x

\begin{aligned} ∴ 5 \times 3 \times x = 8 \times 5 \times 60 \\ \Leftrightarrow x = \frac{(8 \times 5 \times 60)}{(5 \times 3)} \\ \Leftrightarrow x = 160 \end{aligned}

32. 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

Discuss

Solution:

Let the required number of days be x
Less people, More days (Indirect proportion)
Less quantity, Less days ( Direct proportion)

\begin{matrix} People 35 : 50 \\ Quantity 350 : 50 \end{matrix}} :: 30 : x

\begin{aligned} ∴ 35 \times 350 \times x = 50 \times 50 \times 30 \\ \Leftrightarrow x = \frac{(50 \times 50 \times 30)}{(35 \times 350)} \\ \Leftrightarrow x = \frac{300}{49} \\ \Leftrightarrow x = 6 \frac{6}{49} \end{aligned}

33. 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

Discuss

Solution:

Let the required number of days be x
Less working hours, More days (Indirect Proportion)
More men, Less days (Indirect Proportion)

\begin{matrix} Working hours 4 : 8 \\ Men 18 : 12 \end{matrix}} :: 30 : x

\begin{aligned} ∴ 4 \times 18 \times x = 8 \times 12 \times 30 \\ \Leftrightarrow x = \frac{(8 \times 12 \times 30)}{(4 \times 18)} \\ \Leftrightarrow x = 40 \end{aligned}

34. 5 persons can prepare an admission list in 8 days working 7 hours a day. If 2 persons join them so as to complete the work in 4 days, they need to work per day for ?

A. 8 hours

B. 9 hours

C. 10 hours

D. 12 hours

Discuss

Solution:

Let the number of working hours per day be x
More persons, Less working hours ( Indirect proportion)
Less days, More working hours (Indirect proportion)

\begin{matrix} Persons   7 : 5 \\ Quantity  4 : 8 \end{matrix}} :: 7 : x

\begin{aligned} ∴ 7 \times 4 \times x = 5 \times 8 \times 7 \\ \Leftrightarrow x = \frac{(5 \times 8 \times 7)}{(7 \times 4)} \\ \Leftrightarrow x = 10 \end{aligned}

35. 4 persons can prepare an admission list in 8 days working 7 hours a day. If 3 persons join them so as to complete the work in 4 days, they need to work per day for ?

A. 6 hours

B. 8 hours

C. 10 hours

D. 12 hours

Discuss

Solution:

Let the number of working hours per day be x
More persons, Less working hours ( Indirect proportion)
Less days, More working hours (Indirect proportion)

\begin{matrix} Persons   7 : 4 \\ Quantity  4 : 8 \end{matrix}} :: 7 : x

\begin{aligned} ∴ 7 \times 4 \times x = 4 \times 8 \times 7 \\ \Leftrightarrow x = \frac{(4 \times 8 \times 7)}{(7 \times 4)} \\ \Leftrightarrow x = 8 \end{aligned}

36. 3 pumps , working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day ?

A. 9

B. 10

C. 11

D. 12

Discuss

Solution:

Let the required number of working hours per day be x
More pumps, Less working hours per day (Indirect proportion)
Less days, More working hours per day (Indirect proportion)

\begin{matrix} Pumps  4 : 3 \\ Days 1 : 2 \end{matrix}} :: 8 : x

\begin{aligned} ∴ 4 \times 1 \times x = 3 \times 2 \times 8 \\ \Leftrightarrow x = \frac{(3 \times 2 \times 8)}{(4)} \\ \Leftrightarrow x = 12 \end{aligned}

37. If 5 men or 7 women can earn Rs. 5250 per day, how much would 7 men and 13 women earn per day ?

A. Rs. 11600

B. Rs. 11700

C. Rs. 16100

D. Rs. 17100

Discuss

Solution:

Let the required earning be Rs. x
5 men = 7 women
7 men =

(\frac{7}{5} \times 7)

women =

\frac{49}{5}

women
∴ (7 men and 13 women)

\begin{aligned} = (\frac{49}{5} + 13) women \\ = \frac{114}{5} women \end{aligned}

Now, More women, More earning (Direct proportion)

\begin{aligned} ∴ 7 : \frac{114}{5} :: 5250 : x \\ \Leftrightarrow 7 x = (\frac{114}{5} \times 5250) \\ \Leftrightarrow 7 x = 119700 \\ \Leftrightarrow x = 17100 \end{aligned}

38. 3 men or 6 women can do a piece of work in 20 days. In how days will 12 men and 8 women do the same work ?

A. $3 \frac{1}{2} days$

B. $3 \frac{3}{4} days$

C. $4 days$

D. $5 days$

Discuss

Solution:

Let the required number of days be x
3 men = 6 women
⇒12 men = (2 × 12) women = 24 women
∴ 12 men and 8 women = (24 + 8) women = 32 women
Now, More women, Less days (Indirect Proportion)

\begin{aligned} ∴ 32 : 6 :: 20 : x \\ \Leftrightarrow x = (\frac{6 \times 20}{32}) \\ \Leftrightarrow x = \frac{15}{4} \\ \Leftrightarrow x = 3 \frac{3}{4} \end{aligned}

39. 49 pumps can empty a reservoir in $6 \frac{1}{2}$ days, working 8 hours a day. If 196 pumps are used for 5 hours each day, then the same work will be complete in ?

A. 2 days

B. $2 \frac{1}{2}$ days

C. $2 \frac{3}{5}$ days

D. 3 days

Discuss

Solution:

Let the required number of days be x
Then,
More pumps, Less days (Indirect proportion)
Less working hour/day, More days (Indirect proportion)

\begin{matrix} Pumps 196 : 49 \\ Working hour/day   5 : 8 \end{matrix}} :: \frac{13}{2} : x

\begin{aligned} ∴ 196 \times 5 \times x = 49 \times 8 \times \frac{13}{2} \\ \Leftrightarrow x = (49 \times 8 \times \frac{13}{2} \times \frac{1}{196 \times 5}) \\ \Leftrightarrow x = \frac{13}{5} \\ \Leftrightarrow x = 2 \frac{3}{5} \end{aligned}

40. 30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers to finish the same piece of work in 30 days, will be ?

A. 15

B. 21

C. 22

D. 25

Discuss

Solution:

Let the required number of labourers be x
Less working hour/day, More labours (Indirect proportion)
More days, Less labourers (Indirect proportion)

\begin{matrix} Working hours/day  6 : 7 \\ Days 30 : 18 \end{matrix}} :: 30 : x

\begin{aligned} ∴ 6 \times 30 \times x = 7 \times 18 \times 30 \\ \Leftrightarrow 6 x = 126 \\ \Leftrightarrow x = 21 \end{aligned}

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