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Question Detail
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 ?
- 34 days
- 40 days
- 46 days
- 50 days
Answer: Option B
Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
\begin{aligned}
\begin{bmatrix}Cows & 1 & 40 \\Bags & 40 & 1 \end{bmatrix} :: 40 : x \\
=> x * 40 * 1= 40 * 1 * 40 \\
=> x = 40
\end{aligned}
1. In a hostel, Food was available for 2000 students for 54 days, but after 15 days more students joined hostel and food lasts only for 20 more days. Determine how many students came in hostel ?
- 1650
- 1700
- 1900
- 2100
Answer: Option C
Explanation:
As it is given that food is there for 54 days for 2000 students,
But after 15 days, remaining food was sufficient for 2000 students for 39 days only ( as 54-15 = 39 )
Let x number of students came in hostel after 15 days,
=> Total number of students after 15 days = 2000 + x
=> Remaining food was enough for (2000 + x) students for 20 days
So here is indirect proportion, as more people and less food
=> 2000 : ( 2000 + x ) :: 20 : 39
=> 2000 * 39 = ( 2000 + x ) * 20
=> 3900 = 2000 + x
=> x = 3900 - 2000
=> x = 1900
2. 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 ?
- 12
- 14
- 16
- 18
Answer: Option C
Explanation:
Please always remember, that what exactly we need to calculate before applying chain formula. As in this question we need to find how many mats, RIGHT !
So we will compare everything with "number of mats"
As,
More men, More number of mats (Direct Proportion)
More days, More number of mats (Direct Proportion)
So, it can be solved as,
\begin{aligned}
\begin{bmatrix}Weavers & 4 & 8 \\Days & 4 & 8 \end{bmatrix} :: 4 : x \\
=> x*4*4 = 8*8*4 \\
=> x = 16
\end{aligned}
3. An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?
- 194 seconds
- 195 seconds
- 196 seconds
- 197 seconds
Answer: Option B
Explanation:
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,
\begin{aligned}
0.128 : 1 :: 25 : x
=> x = \frac{25*1}{0.128} \\
=> x = 195.31
\end{aligned}
So time will be approx 195 seconds
4. If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate ?
- xd
- yd
- yd/x
- x/yd
Answer: Option C
5. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
- 24 days
- 28 days
- 34 days
- 35 days
Answer: Option A
Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
27 : 36 :: 18 : x
[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
\begin{aligned}
x = \frac{36*18}{27} \\
x = 24
\end{aligned}
So 24 days will be required to get work done by 27 men.
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