Direct And Inverse Proportions- 2 - Free MCQ Practice Test with solutions,

Since y=x, if y increases , x also increases and if y decreases x also decreases. So they are directly related.

Let the remaining food last for x days
500 men had provision for = (27 - 3) = 24 days
(500 + 300) men had provision for x days
More men, Less days (Indirect proportion)
∴ 800 : 500 :: 24 : x
⇔ (800 × x) = (500 × 24)
⇔ x = (500 × 24)/800
⇔ x = 15

Let's solve the problem using the concept of direct proportion.

Given:

• 12 men can dig an 8-meter-long trench in one day.
• We need to find the number of men required to dig a 50-meter-long trench in one day.

Step 1: Establish the proportion

The number of men required is directly proportional to the length of the trench.

Let x be the number of men required to dig the 50-meter trench.

Men∝Length of trench

So,

Food for 320 students= 80 days

20 students left the campus

Number of students = 320 - 20 = 300 students

Food will last for (80 - 20) = 60 days fpr 320 students

Food will last for X days for 300 students

⇒ X = (320 x 60)/300 = 64

Food for 300 students= 64 days

45 minutes = 45/60 hour = 3/4 hour
25 minutes = 25/60 hour = 5/12 hour
distance = speed x time
as distance travel is same
40x3/4=ax5/12
solve it and you will get a=72 km/h

Determine the cost per meter: Divide the total cost by the number of meters.
Rs 210 ÷ 5 metres = Rs 42 per metre.

Calculate the cost for 2 meters: Multiply the cost per meter by 2.
Rs 42 × 2 = Rs 84.

Conclusion: Therefore, the cost of 2 meterss of cloth is Rs 84.

The ratio given is 1 part red pigment to 8 parts base, which simplifies to 1:8.

To find the amount of base needed for 4 parts of red pigment, use the following calculation:

• Base = 4 × 8 = 32

Thus, 32 parts of base are required.

To determine how long it will take for 5 pipes to fill the tank, we first calculate the rate at which the pipes fill the tank.

1. Convert 1 hour 20 minutes into hours:

   1 hour 20 minutes = 1 + 20/60 = 4/3 hours

2. Calculate the filling rate of one pipe:

   • Total work = 1 tank
   • Rate of 6 pipes = Work/Time = 1/(4/3) = 3/4 tanks per hour
   • Rate of one pipe = Rate of 6 pipes/6 = (3/4)/6 = 1/8 tanks per hour

3. Calculate the time required for 5 pipes to fill the tank:

   • Rate of 5 pipes = 5 x (1/8) = 5/8 tanks per hour
   • Time = Work/Rate = 1/(5/8) = 8/5 hours = 1.6 hours
   • Convert hours to minutes:
   • 0.6 x 60 = 36 minutes
   • Total time = 1 hour 36 minutes = 96 minutes

Thus, it will take 5 pipes 96 minutes to fill the tank.

When two quantities x and y increase or decrease together while maintaining a constant ratio, they are in direct proportion. This relationship can be expressed as:

• y = kx,
• where k is the constant of proportionality.

When two quantities x and y are inversely proportional, an increase in one results in a proportional decrease in the other. This ensures that their product remains constant.

This relationship can be expressed mathematically as:

• x × y = k, where k is a constant.

Therefore, the correct term for this relationship is 'inverse proportion.'

Since the pole and the tree cast shadows under similar conditions, their heights and shadow lengths are proportional. This means that the ratio of the height of the pole to its shadow is equal to the ratio of the height of the tree to its shadow. Set up the proportion as 14/10 = Tree Height/15. By cross-multiplying, we get Tree Height = (14 × 15) divided by 10. Calculating this gives 210/10 = 21 metres.

Therefore, the height of the tree is 21 metres.

It’s direct proportion
 Bottles

Since the number of sugar crystals is directly proportional to the weight of sugar, we can set up the following relationship:

Weight of sugar / Number of crystals = k

Where k is a constant.
Using the given information:

k=2 kg / 9×10⁶ crystals

Let y be the number of crystals in 1.2 kg of sugar. Again using the direct proportion:

1.2 kg / y = 2 kg / 9×10⁶ crystals

Cross-multiplying gives:

1.2 × ( 9×10⁶ ) = 2 × y

Calculating the left side:

10.8 × 10⁶ = 2y

Now, solving for y:

y = 10.8×10⁶ / 2 = 5.4 × 10⁶

It is an inverse relation
days

Given, price of 5m cloth = 210
price of 1m cloth = 210 / 5 = 42
price of 4m cloth = 4×42
= RS.168 

It is direct proportion,
So, 1/8 = 7/y
y = 8 * 7
y = 56 parts of base.

Number of person = 100, Number of days = 20, = 100 * 20
Number of person = 125  (∵ 25 student join), let Number of days = x = 125 * X
So, 100 * 20 = 125 * X
or 2000 = 125x
or, 125x =  2000

∴ X = 2000/125 = 16
Therefore, that the last provisions will 16 dyas.