Direct And Inverse Proportions- 1 - Free MCQ Practice Test with solutions,

If the ratio (x/y) of two variables (x and y) is equal to a constant (k = yx), then the variable in the numerator of the ratio (y) is the product of the other variable and the constant (y = k⋅x). In this case y is said to be directly proportional to x with proportionality constant k.

We are given:

8 : 12 :: 6 : a

That means
8/12 = 6/a

Cross multiply:
8a = 12 × 6
8a = 72
a = 72 ÷ 8
a = 9

Clearly, 

∴x and y are directly proportional as x/y is a constant.

Given:
We know that 3 men can do the work in 16 days, which is the same as 6 women
Therefore, 3 men = 6 women
⇒ 1 man = 2 women
Now, for 12 men:
12 men = 12 × 2 = 24 women 
Now, Total workers:
24 women + 8 women = 32 women

Using Inverse Proportions:
As Given 6 women take 16 days,
let us assume 32 women take x days 

Women × Days = constant
6 × 16 = 32 × x
96 = 32 × x
x = 96 ÷ 32
x = 3

So, 12 men and 8 women will take 3 days.

Given:

• Speed₁ = 54 km/h

• Time₁ = 2.5 h

• Distance is the same.

Since distance = speed × time,
for the same distance, speed and time are inversely proportional.

So,

Time = 3 hours

Correct answer: (b) 3 hours

This is a question of direct proportion as with increase in depth of digging the number of men will increase
So, in direct proportion the constant value is given by X/ Y
12/8 = a/50 (where a is the number of men to be employed)
12 X 50 = 8 X a
600 = 8 X a
600/ 8 = a
75 men = a

Cost of 18 pens = Rs 234
So Cost of 1 pen = 234/18=13
So a dozen pens (12 pens) will cost =
12 X13 = Rs 156

Since wages are directly related to no. of days , we apply direct variation

The total amount of food can be calculated in person-days. Initially, it is:

• 40 people * 10 days = 400 person-days.

When 50 people share the same food, the duration can be calculated as follows:

• 400 person-days / 50 people = 8 days.

Therefore, the food will last for 8 days.