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If two quantities x and y vary directly, then
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.
Observe the given table.
What can be said about x and y?
Clearly,
∴x and y are directly proportional as x/y is a constant.
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?
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.
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
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?
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
If the cost of 18 pens is Rs. 234, a dozen pen will cost
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
Raju earns Rs 1440, if he works for 12 days. If he works for 30 days, he will earn
Since wages are directly related to no. of days , we apply direct variation
There is enough food to last for 40 people for 10 days. If 10 more people join them, the food will last for
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:
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