Test: Direct And Inverse Proportions- 1

QUESTION: 1

If two quantities x and y vary directly, then

A.
x * y is constant
B.
x/y is constant
C.
x − y is constant
D.
x + y is constant

Solution:

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.

QUESTION: 2

If 8:12::6:a, the value of a is

A.
12
B.
10
C.
9
D.
8

Solution:

QUESTION: 3

Observe the given table.

What can be said about x and y?

A.
x and y are directly proportional.
B.
x is inversely proportional to y.
C.
y is inversely proportional to x.
D.
There is no proportionality between x and y.

Solution:

Clearly,

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

QUESTION: 4

If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?

A.
4 days
B.
5 days
C.
3 days
D.
2 days.

Solution:

Given, 3 men = 6 women
Now, 12 men = (12 x 6)/3 = 24 women
And 12 men + 8 women = 24 women + 8 women = 32 women.
If, 6 women can do a piece of work in 16 days ---------- (given)
32 women will do that piece of work in = 6 x (16/32) = 3 days
12 men and 8 women will do the piece of work in 3 days.

QUESTION: 5

A car is traveling at a speed of 54 km/ hour, covers a distance in 2.5 hours. At a speed of 45 km/hr, it covers the same distance in

A.
1 hour
B.
3 hours
C.
2 hours
D.
None of thes

Solution:

QUESTION: 6

12 men can dig 8 meters long trench in a day. How many men should be employed for digging 50 meter long trench of the same type in one day?

A.
50
B.
75
C.
25
D.
None of these

Solution:

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

QUESTION: 7

If the cost of 18 pens is Rs. 234, a dozen pen will cost

A.
Rs 144
B.
Rs 156
C.
Rs 192
D.
Rs 180

Solution:

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

QUESTION: 8

Raju earns Rs 1440, if he works for 12 days. If he works for 30 days, he will earn

A.
Rs 2400
B.
Rs 3600
C.
Rs 4800
D.
None of these

Solution:

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

QUESTION: 9

There is enough food to last for 40 people for 10 days. If 10 more people join them, the food will last for

A.
10 days
B.
12 days
C.
8 days
D.
None of these

Solution:

QUESTION: 10

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in: