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11. A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:

A. 10 m

B. 12.5 m

C. 17.5 m

D. 21.25 m

Discuss

Solution:

Let the height of the building x metres.
Less lengthy shadow, Less in the height (Direct Proportion)

\begin{aligned} ∴ 40.25 : 28.75 :: 17.5 : x \\ \Rightarrow 40.25 \times x = 28.75 \times 17.5 \\ \Rightarrow x = \frac{28.75 \times 17.5}{40.25} \\ \Rightarrow x = 12.5 \end{aligned}

12. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

A. 20

B. 30

C. 40

D. 50

Discuss

Solution:

There is a meal for 200 children
150 children have taken the meal
Remaining meal is to be catered to 50 children
Now,
200 children = 120 men
∴ 50 children

\begin{aligned} = (\frac{120}{200} \times 50) men \\ = 30 men \end{aligned}

13. 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. 204

D. 488

Discuss

Solution:

Le the required time be x seconds.
More metres, More time (Direct Proportion)

\begin{aligned} ∴ 0.128 : 25 :: 1 : x \\ \Rightarrow 0.128 x = 25 \times 1 \\ x = \frac{25}{0.128} = \frac{25 \times 1000}{128} \\ \Rightarrow x = 195.31 \end{aligned}

∴ Required time = 195 sec (approximately)

14. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

A. 12

B. 18

C. 22

D. 24

Discuss

Solution:

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

\begin{aligned} ∴ 27 : 36 :: 18 : x \\ \Rightarrow 27 \times x = 36 \times 18 \\ \Rightarrow x = \frac{36 \times 18}{27} \\ \Rightarrow x = 24 \end{aligned}

15. 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

A. 4

B. 8

C. 12

D. 16

Discuss

Solution:

Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)

\begin{matrix} Wavers 4 : 8 \\ Days 4 : 8 \end{matrix}} :: 4 : x

\begin{aligned} ∴ 4 \times 4 \times x = 8 \times 8 \times 4 \\ \Rightarrow x = \frac{8 \times 8 \times 4}{4 \times 4} \\ \Rightarrow x = 16 \end{aligned}

16. 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

Discuss

Solution:

Let the required price be Rs. x
More mangoes, More price (Direct proportion)

\begin{aligned} ∴ 357 : (49 \times 12) :: 1517.25 : x \\ \Leftrightarrow 357 x = (49 \times 12 \times 1517.25) \\ \Leftrightarrow x = \frac{(49 \times 12 \times 1517.25)}{357} \\ \Leftrightarrow x = 2499 \end{aligned}

Hence, the approximate price is Rs. 2500

17. 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

Discuss

Solution:

Let the required time be x seconds
Then,
More metres, More time (direct proportion)

\begin{aligned} ∴ 0.128 : 25 :: 1 : x \\ \Leftrightarrow x = \frac{25}{0.128} \\ \Leftrightarrow x = \frac{25 \times 1000}{128} \\ \Leftrightarrow x = 195.31 \end{aligned}

`
∴ Required time =195 seconds (approx)

18. A snapshot $1 \frac{7}{8} \times 2 \frac{1}{2}$ is to be enlarged so that the longer dimension is 4. What will be the dimension of the shorter side ?

A. $2 \frac{3}{8}$

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

C. $3$

D. $3 \frac{3}{8}$

Discuss

Solution:

Let the dimension of the shorter side be x
More is the longer side, More is the shorter side (Direct proportion)

\begin{aligned} ∴ 2 \frac{1}{2} : 4 :: 1 \frac{7}{8} : x \\ \Leftrightarrow \frac{5}{2} x = 4 \times \frac{15}{8} \\ \Leftrightarrow x = (\frac{15}{2} \times \frac{2}{5}) \\ \Leftrightarrow x = 3 \end{aligned}

19. 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

Discuss

Solution:

Total number of days = (30 + 31 + 30) = 91
Let the number of bananas be x
More days, More bananas (Direct proportion)

\begin{aligned} ∴ 7 : 91 :: 651 : x \\ \Rightarrow 7 x = 91 \times 651 \\ \Rightarrow x = (\frac{91 \times 651}{7}) \\ \Rightarrow x = 8463 \end{aligned}

20. If $\frac{4}{9}$ th of a bucket is filled in 1 minute, the rest of it will be filled in ?

A. $1 minute$

B. $\frac{9}{4} minute$

C. $\frac{5}{4} minute$

D. $\frac{4}{5} minute$

Discuss

Solution:

Remaining part

\begin{aligned} = (1 - \frac{4}{9}) \\ = \frac{5}{9} \end{aligned}

Let the required time be x minutes
More volume to be filled , More time taken (Direct proportion)

\begin{aligned} ∴ \frac{4}{9} : \frac{5}{9} :: 1 : x \\ \Rightarrow \frac{4}{9} x = \frac{5}{9} \\ \Rightarrow x = (\frac{5}{9} \times \frac{9}{4}) \\ \Rightarrow x = \frac{5}{4} \end{aligned}

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