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QUESTION: 1

If two quantities x and y vary directly, then

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

Solution:

QUESTION: 3

Observe the given table.

What can be said about 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?

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

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?

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

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

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

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:

Solution:

### Direct and Inverse Proportions

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