The sum of a number and its reciprocal is 26 5 . Find the number.

Let the number be x so the reciprocal of the number is 1 x . According to the question, x + 1 x = 26 5 ⇒ x 2 + 1 x = 26 5 ⇒ 5 x 2 + 1 = 26 x ⇒ 5 x 2 + 5 - 26 x = 0 ⇒ 5 x 2 - 26 x + 5 = 0 By using quadratic formula, we get x = - - 26 ± - 26 2 - 4 × 5 × 5 2 × 5 ⇒ x = 26 ± 676 - 100 10 ⇒ x = 26 ± 576 10 ⇒ x = 26 ± 24 10 So, ⇒ x = 26 + 24 10 = 5 Or, x = 26 - 24 10 = 1 5 So, the number is 5 or 1 5 .

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Two trains leave a railway station at the same time. The first train travels towards west and the second train towards north. The first train travels $5 km / hr$ faster than the second train. If after two hours they are $50 km$ apart, find the speed of each train.

Important Questions on Quadratic Equations

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

The altitude of a right triangle is

7 cm

less than its base. If the hypotenuse is

13 cm

, find the other two sides.

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is $20 years$ . Four years ago, the product of their ages in years was $48 .$

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

A dealer sells an article for

₹ 16

and loses as much per cent as the cost price of the article. Find the cost price of the article.

HARD

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

A motor boat whose speed is $18 km / hour$ in still water takes $1 hour$ more to go $24 km$ upstream than to return downstream to the same spot. If the speed of the stream is $x km / hour$ , find $x$ .

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

₹ 7500

were divided equally among a certain number of children. Had there been

20

less children, each would have received

100

more. Find the original number of children.

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Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

A train travels

360 km

at a uniform speed. If the speed had been

10 km / h

more, it would have taken

3

hours less for the same journey. Find the speed(in

km / h

) of the train.

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

Find two consecutive odd positive integers, sum of whose squares is

290

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

Find two consecutive odd positive integers, sum of whose square is $290$ .

HARD

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

The sum of the areas of two squares is $400 s q . m .$ If the difference between their perimeters is $16 m$ , find the sides of two squares

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

Find two consecutive natural numbers whose product is

20

EASY

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

If the price of

1

dozen pens is reduced by

₹ 6

, then

3

more pens will be bought at

₹ 30

. Calculate the price of one dozen pens (in

₹

) before the reduction of price.

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Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

Two water taps together can fill a tank in

1 \frac{7}{8}

hours. The tap with longer diameter takes

2

hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

The sum of a number and its reciprocal is $\frac{26}{5}$ . Find the number.

EASY

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

The product of two consecutive positive integers is

30

. This can be expressed algebraically as

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

Find two consecutive odd positive integers, sum of whose squares is

394

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

x^{4} - 83 x^{2} + 1 = 0

, then a value of

x^{3} - x^{- 3}

is:

HARD

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

Two water taps together can fill a tank in

9 \frac{3}{8}

hours. The tap of larger diameter takes

10

hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

The sum of the squares of two consecutive odd positive integers is

650

. Find the numbers

HARD

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

In a flight of

600 km

, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by

200 km / hr

and time of flight increased by

30

minutes. Find the original duration of flight.

MEDIUM

Mathematics>Algebra>Quadratic Equations>Word Problems on Quadratic Equation

A plane left

30

minutes late than its scheduled time and in order to reach the destination

1500 k m

away in time, it had to increase its speed by

100 k m / h

from the usual speed. Find its usual speed.

Two trains leave a railway station at the same time. The first train travels towards west and the second train towards north. The first train travels 5 km/hr faster than the second train. If after two hours they are 50 km apart, find the speed of each train.

Important Questions on Quadratic Equations

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Two trains leave a railway station at the same time. The first train travels towards west and the second train towards north. The first train travels $5 km / hr$ faster than the second train. If after two hours they are $50 km$ apart, find the speed of each train.