Direct and Inverse Proportion - Jharkhand Board (JAC) STD 8 Maths Questions

Both x and y are in direct proportion, then$\frac{1}{\text{x}}$ and $\frac{1}{\text{y}}$ are:

A
In indirect proportion.
✓
In indirect proportion.
C
Neither in direct nor in inverse proportion.
D
Sometimes in direct and sometimes in inverse proportion.

Answer: B.

Both $u$ and $v$ vary directly with each other. When $u$ is $10, v$ is $15,$ which of the following is not a possible pair of corresponding values of $u$ and $v?$

A
$2$ and $3$
B
$8$ and $12$
✓
$15$ and $20$
D
$25$ and $37.5$

Answer: C.

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Q 3M.C.Q. [1 Marks Each]1 Mark

100 persons had food provision for $24$ days. If $20$ persons left the place, the provision will last for

✓
$30$ days
B
$\frac{96}{5}$days
C
$120$ days
D
$40$ days

Answer: A.

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Q 4M.C.Q. [1 Marks Each]1 Mark

Both $x$ and $y$ vary inversely with each other. When $x$ is $10, y$ is $6,$ which of the following is not a possible pair of corresponding values of $x$ and $y?$

A
$12$ and $5$
B
$15$ and $4$
C
$25$ and $2.4$
✓
$45$ and $1.3$

Answer: D.

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Q 5M.C.Q. [1 Marks Each]1 Mark

If the distance travelled by a rickshaw in one hour is $10\ km,$ then the distance travelled by the same rickshaw with the same speed in one minute is:

A
$\frac{250}{9}\text{m}$
B
$\frac{500}{9}\text{m}$
C
$1000\text{m} $
✓
$\frac{500}{3}\text{m}$

Answer: D.

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Q 62 Marks Questions2 Marks

If a deposit of $Rs 2,000$ earns an interest of $Rs. 500$ in $3$ years, how much interest would a deposit of $Rs 36,000$ earn in $3$ years with the same rate of simple interest?

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Q 72 Marks Questions2 Marks

There are $20$ grams of protein in $75$ grams of sauted fish. How many grams of protein is in $225\ gm$ of that fish?

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Q 82 Marks Questions2 Marks

A car travels a distance of $225\ km$ in $25$ litres of petrol. How many litres of petrol will be required to cover a distance of $540$ kilometres by this car?

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Q 92 Marks Questions2 Marks

In a hostel of $50$ girls, there are food provisions for $40$ days. If $30$ more girls join the hostel, how long will these provisions last?

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Q 102 Marks Questions2 Marks

From the following table, determine if $x$ and $y$ are in direct proportion or not.

$x$	$3$	$6$	$15$	$20$	$30$
$y$	$12$	$24$	$45$	$60$	$120$

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Q 113 Marks Question3 Marks

If Naresh walks $250$ steps to cover a distance of $200$ metres, find the distance travelled in $350$ steps.

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Q 123 Marks Question3 Marks

Here is a key board of a harmonium:

$a.$ Find the ratio of white keys to black keys on the keyboard.
$b.$ What is the ratio of black keys to all keys on the given keyboard.
$c.$ This pattern of keys is repeated on larger keyboard. How many black keys would you expect to find on a keyboard with $14$ such patterns.

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Q 133 Marks Question3 Marks

A contractor undertook a contract to complete a part of a stadium in $9$ months with a team of $560$ persons. Later on, it was required to complete the job in $5$ months. How many extra persons should he employ to complete the work?

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Q 143 Marks Question3 Marks

Find the values of $x$ and $y$ if $a$ and $b$ are in inverse proportion:
$a. 12 x 8$
$b. 30 5y$

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Q 153 Marks Question3 Marks

Many schools have a recommended students-teacher ratio as $35:1.$ Next year, school expects an increase in enrolment by $280$ students. How many new teachers will they have to appoint to maintain the students-teacher ratio?

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Q 165 Marks Questions5 Marks

Ravi starts for his school at $8:20a.m$. on his bicycle. If he travels at a speed of $10\ km/h$, then he reaches his school late by $8$ minutes but on travelling at $16\ km/h$ he reaches the school $10$ minutes early. At what time does the school start?

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Q 175 Marks Questions5 Marks

The table shows the time four elevators take to travel various distances. Find which elevator is fastest and which is slowest.

	Distance (m)	Time (sec.)
Elevator $- A$	$435$	$29$
Elevator $- B$	$448$	$28$
Elevator $- C$	$130$	$10$
Elevator $- D$	$85$	$5$

How much distance will be travelled by elevators $B$ and $C$ seperately in $140$sec? Who travelled more and by how much?

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Q 185 Marks Questions5 Marks

If $a$ and $b$ vary inversely to each other, then find the values of $p, q, r ; x, y, z$ and $l, m, n.$

$a$	$6$	$8$	$q$	$50$
$b$	$18$	$p$	$39$	$r$

$a$	$2$	$y$	$6$	$10$
$b$	$x$	$12.5$	$15$	$z$

$a$	$l$	$9$	$n$	$6$
$b$	$5$	$m$	$25$	$10$

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Q 195 Marks Questions5 Marks

Match each of the entries in Column $I$ with the appropriate entry in Column $II$

S.No	Column $I$	S.No	Column II
$1.$	x and y vary inversely to each other	$A.$	$\frac{\text{x}}{\text{y}}=\text{constant}$
$2.$	Mathematical representation of inverse variation of quantities $p$ and $q$	$B.$	$y$ will increase in proportion
$3.$	Mathematical representation of direct variation of quantities $m$ and $n$	$C.$	$xy$ = Constant
$4.$	When $x = 5, y = 2.5$ and when $y = 5, x = 10$	$D.$	$\text{p} \propto\frac{1}{\text{q}}$
$5.$	When $x = 10 , y = 5$ and when $x = 20, y = 2.5$	$E.$	$y$ will decrease in proportion
$6.$	x and y vary directly with each other	$F.$	$x$ and $y$ are directly proportional
$7.$	If x and y vary inversely then on decreasing x	$G.$	$\text{m }\alpha \text{ n}$
$8.$	If x and y vary directly then on decreasing	$H.$	$x$ and $y$ vary inversely
		$I.$	$\text{p } \alpha \text{ q}$
		$J.$	$\text{m }\alpha \frac{1}{\text{n}}$

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Q 201 Marks Question1 Mark

From the following table, determine if $x$ and $y$ are in direct proportion or not.

$X$	$1$	$4$	$9$	$20$
$Y$	$1.5$	$6$	$13.5$	$30$

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Q 211 Marks Question1 Mark

Income tax and the income.

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Q 221 Marks Question1 Mark

It is given that l varies directly as $m?$ Find the constant of proportion $(k),$ when l is $6$ then $m$ is $18.$

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Q 231 Marks Question1 Mark

The number of people working and the time to complete a given work

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Q 241 Marks Question1 Mark

Area of the walls of a room and the cost of white washing the walls.

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Q 25BLANKS [1 Marks Each]1 Mark

If $x$ varies inversely as $y,$ then

$x$	-	$60$
$y$	$2$	$10$

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Q 26BLANKS [1 Marks Each]1 Mark

If $d$ varies directly as $t^2$, then we can write $dt^2= k$, where $k$ is some constant.

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Q 27BLANKS [1 Marks Each]1 Mark

Both $x$ and $y$ are said to vary _______ with each other if for some positive number $k, xy = k.$

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Q 28BLANKS [1 Marks Each]1 Mark

If $x$ and $y$ are in inverse proportion, then $(x + 1)$ and $(y + 1)$ are also in inverse proportion.

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Q 29BLANKS [1 Marks Each]1 Mark

On increasing $a, b$ increases in such a manner that $\frac{\text{a}}{\text{b}}$ remains _____ and positive, then $a$ and $b$ are said to vary directly with each other.

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Direct and Inverse Proportion question types

Direct and Inverse Proportion questions

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Direct and Inverse Proportion Maths - Direct and Inverse Proportion

Direct and Inverse Proportion question types

Direct and Inverse Proportion questions

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