Question Detail

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

1. 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

2. 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.

3. 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 the remaining meal ?

38 men
32 men
34 men
30 men

Answer: Option D

Explanation:

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

So, 50 Children = 120/200 * 50 = 30 men

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

12 metre
12.5 metre
13.5 metre
14 metre

Answer: Option B

Explanation:

Less shadow, Less Height (Direct Proportion)
So, let height of building be x metre
then,
\begin{aligned}
40.25 : 17.5 :: 28.75 : x \\

=> x = \frac{17.5*28.75}{40.25} \\
=> x = 12.5
\end{aligned}

So height of building should be 12.5 metre

5. 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}