Test: Direct and Inverse Variations - Class 8 MCQ

The one-day work formula is calculated as the total work divided by the total time needed to complete that work. This helps determine how much work can be done in a single day.

The unitary method simplifies direct variation problems by first determining the value of one unit and then using it to find the total for multiple units.

In direct variation, the relationship between the two quantities is linear, represented graphically by a straight line passing through the origin.

The unitary method in direct variation involves finding the value of one unit and then multiplying this value by the number of units required to find the total.

The calculations show that 70 kg of ration can sustain approximately 7 students for 25 days based on the initial ratio of ration to students.

After working together for 20 days, they complete part of the work. A's remaining work rate helps determine that A will take 44 more days to finish the task alone.

Direct variation occurs when one quantity increases and the other also increases, or when one decreases and the other decreases. This relationship is characterized by a constant ratio between the two variables.

To build a wall double in size in 75 days, calculations show that 40 men are needed (30 men for the original wall, adjusted for size and time).

Time is calculated using the formula: Time = Distance/Speed. Therefore, it will take 120 km / 60 km/h = 2 hours.

Doubling the number of workers halves the time required to complete the task due to inverse variation, resulting in 6 days for 8 workers.

After 20 days, provisions for 300 men would last 70 days. For 250 men, the remaining provisions last 21,000 days divided by 250, resulting in 84 days of food.

A constant ratio of 3:1 indicates that the two quantities exhibit direct variation, meaning that as one increases, the other also increases proportionally.

Using the inverse relationship, if the sum is constant, each boy will receive ₹62.50 when divided among 60 boys instead of 50.

If 3 men complete 1/30 of the work in one day, they will finish the entire work in 30 days.

In the arrow method, for inverse proportion, one arrow points upward and the other downward to indicate the inverse relationship between the quantities.