Using properties of proportion find x : y , given: x 2 + 2 x 2 x + 4 = y 2 + 3 y 3 y + 9

Using properties of proportion we have to find x : y , given: x 2 + 2 x 2 x + 4 = y 2 + 3 y 3 y + 9 Applying componendo and dividendo, ⇒ x 2 + 2 x + 2 x + 4 x 2 + 2 x - 2 x - 4 = y 2 + 3 y + 3 y + 9 y 2 + 3 y - 3 y - 9 ⇒ ( x + 2 ) 2 ( x - 2 ) ( x + 2 ) = ( y + 3 ) 2 ( y - 3 ) ( y + 3 ) ⇒ ( x + 2 ) 2 ( x - 2 ) 2 = ( y + 3 ) 2 ( y - 3 ) 2 [ because when we split ( x + 2 ) 2 and ( y + 3 ) 2 we will get, x 2 + 4 x + 4 and y 2 + 6 y + 9 ] ⇒ x + 2 x - 2 = y + 3 y - 3 Applying componendo and dividendo again, ⇒ x + 2 + x - 2 x + 2 - x + 2 = y + 3 + y - 3 y + 3 - y + 3 ⇒ 2 x / 4 = 2 y / 6 ⇒ x / 2 = y / 3 ⇒ x / y = 2 / 3 Hence, the ratio is x : y = 2 : 3 .

MEDIUM

Earn 100

Take a squared paper and arrange $48$ squares in a different number of rows as shown below:

Number of rows ( $R$ ) $2$ $3$ $4$ $6$ $8$

Number of columns ( $C$ ) ... ... $12$ $8$ ...

What do you observe? As $R$ increases, $C$ decreases

Is $R_{1} : R_{2} = C_{2} : C_{1}$ ?

Important Questions on Direct and Inverse Proportions

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

Mayank can do a piece of work in

3

days. Sanjay can do the same work in

4

days. The wage for full work is

₹ 350

. If both work together to complete the work, then find out the earning of Sanjay if the wages are paid in proportion to work done.

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

If $p$ persons working $p$ hours a day for each of $p$ days produce $p$ units of work, then the units of the work produced by $q$ persons working $q$ hours a day for each $q$ day is:

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

x

varies as

y z

, then

y

varies inversely as

MEDIUM

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

A vessel contained a solution of acid and water in which water was

64 %

. Four litres of the solution were taken out of the vessel and the same quantity of water was added. If the resulting solution contains

30 %

acid, the quantity(in litres) of the solution, in the beginning in the vessel, was

HARD

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

The cost of milk per litre is $₹ 15$ . Draw the graph for the relation between the quantity and cost. Hence find the cost of $3$ litres of milk..

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

y = 3 + 1.9 x

, and mode of

x

15

, then the mode of

y

is:

MEDIUM

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

A set of farmers can completely harvest a crop in

10

days. However

12

farmers fell ill and now the remaining can do this job in

15

days. Find the original number of farmers.

MEDIUM

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

A device can write $100$ digits in $1$ minute. It starts writing natural numbers. The device is stopped after running it for half an hour. It is found that the last number it was writing, is incomplete. The number is

HARD

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

The cost of milk per litre is $₹ 15$ . Draw the graph for the relation between the quantity and cost. Hence find the proportionality constant.

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

x α y

then

MEDIUM

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

What is that number, which is when added to

7, 16, 43, 79

these numbers become proportional?

MEDIUM

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

A certain sum is divided among A, B and C in such way that A gets Rs.

40

more than half of the sum. B gets Rs.

120

less than three-eighths of the sum and C gets Rs.

200

. What is the total sum?

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

(3 + x) : (5 + x) : (8 + x)

, then find the value of

x

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

A sum of

₹ 549

is to be divided among Priya, Preeti and Sonu in such a way that

3

times Priya's share,

4

times Preeti's share and

7

times Sonu's share are all equal. What is the share of Priya?

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

x^{3} y, x^{2} y^{2}

and

x y^{3}

are in continued proportion.

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

Using properties of proportion find $x : y$ , given:

$\frac{x^{2} + 2 x}{2 x + 4} = \frac{y^{2} + 3 y}{3 y + 9}$

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

a : b = 3 : 4, b : c = 4 : 7

, then

\frac{a + b + c}{c}

is equal to

MEDIUM

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

How much time the minute hand of a clock will take to describe an angle of

\frac{2 π}{3}

radians ?

EASY

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

A car consumes

5.4 litres

of petrol to cover

60.48 km

, how many kilometres be covered with

22 litres

of petrol?

HARD

Mathematics>Algebra>Direct and Inverse Proportions>Inverse Proportion

There are two candles of same length and same size. Both of them burn at uniform rate. The first, one burns in

5

hours and the second one burns in

3

hours. Both the candles are lit together. After how many minutes the length of the first candle is

3

times that of the other?

Number of rows ( $R$ )	$2$	$3$	$4$	$6$	$8$
Number of columns ( $C$ )	...	...	$12$	$8$	...

Take a squared paper and arrange 48 squares in a different number of rows as shown below: Number of rows (R) 2 3 4 6 8 Number of columns (C) ... ... 12 8 ... What do you observe? As R increases, C decreases Is R1:R2=C2:C1?

Important Questions on Direct and Inverse Proportions

Learn and Prepare for any exam you want !

Take a squared paper and arrange $48$ squares in a different number of rows as shown below:

Number of rows ( $R$ ) $2$ $3$ $4$ $6$ $8$

Number of columns ( $C$ ) ... ... $12$ $8$ ...

What do you observe? As $R$ increases, $C$ decreases

Is $R_{1} : R_{2} = C_{2} : C_{1}$ ?