Direct and Inverse Variation — Mental Maths

Fill in the blanks:

(i) Two quantities are said to be in direct variation if an increase (or decrease) in one quantity causes ..... in other quantity.

(ii) Two quantities $x$ and $y$ are said to be in inverse variation if $xy$ is ......

(iii) The total cost of articles varies ..... to the number of articles purchased.

(iv) More work is done in ..... time.

(v) The time taken to finish a work varies ..... to the number of men at work.

(vi) The speed of a moving object varies inversely to the ..... to cover a certain distance.

(vii) The number of articles varies ..... with the cost per article, if a fixed amount is available.

(viii) Remuneration is in ..... of work done.

Answer

(i) Two quantities are said to be in direct variation if an increase (or decrease) in one quantity causes increase (or decrease) in other quantity.

(ii) Two quantities $x$ and $y$ are said to be in inverse variation if $xy$ is constant.

(iii) The total cost of articles varies directly to the number of articles purchased.

(iv) More work is done in more time.

(v) The time taken to finish a work varies inversely to the number of men at work.

(vi) The speed of a moving object varies inversely to the time taken to cover a certain distance.

(vii) The number of articles varies inversely with the cost per article, if a fixed amount is available.

(viii) Remuneration is in proportion of work done.

State whether the following statements are true (T) or false (F):

(i) Two quantities $x$ and $y$ are said to be in inverse variation if $\dfrac{x}{y}$ is constant.

(ii) Number of days needed to complete the work = $\dfrac{1}{\text{one day's work}}$

(iii) Two quantities $x$ and $y$ are said to be in direct variation if $x = ky$, where $k$ is constant of variation.

(iv) The work done varies inversely to the number of men at work.

(v) In the given time, the distance covered by a moving object varies directly to its speed.

(vi) More the money deposited in a bank, more is the interest earned.

(vii) If the number of articles purchased increases the total cost decreases.

(viii) At the same time length of shadow is in direct variation with length of the object.

(ix) The distance covered varies inversely to the consumption of petrol.

Answer

(i) Two quantities $x$ and $y$ are said to be in inverse variation if $xy$ is constant and not if $\dfrac{x}{y}$ is constant.

Hence, the given statement is false.

(ii) Number of days needed to complete the work = $\dfrac{1}{\text{one day's work}}$

Hence, the given statement is true.

(iii) Two quantities $x$ and $y$ are in direct variation if $\dfrac{x}{y}$ is constant, i.e. if $x = ky$, where $k$ is constant of variation.

Hence, the given statement is true.

(iv) More the number of men at work, more will be the work done. So, the work done varies directly and not inversely to the number of men at work.

Hence, the given statement is false.

(v) In the given time, more the speed of a moving object, more will be the distance covered by it.

Hence, the given statement is true.

(vi) More the money deposited in a bank, more will be the interest earned on it.

Hence, the given statement is true.

(vii) More the number of articles purchased, more will be the total cost. So, the total cost increases and does not decrease.

Hence, the given statement is false.

(viii) At the same time, more the length of the object, more will be the length of its shadow.

Hence, the given statement is true.

(ix) More the consumption of petrol, more will be the distance covered. So, the distance covered varies directly and not inversely to the consumption of petrol.

Hence, the given statement is false.