The sum of a number and its reciprocal is 2 1 30 . Find the number.

Consider, the required number be x . According to the given condition, x + 1 x = 2 1 30 ⇒ ( x 2 + 1 ) x = 61 30 ⇒ 30 x 2 + 30 = 61 x ⇒ 30 x 2 - 61 x + 30 = 0 ⇒ 30 x 2 - 36 x - 25 x + 30 = 0 ⇒ 6 x ( 5 x - 6 ) - 5 ( 5 x - 6 ) = 0 ⇒ ( 5 x - 6 ) ( 6 x - 5 ) = 0 ⇒ 5 x - 6 = 0 or 6 x - 5 = 0 ⇒ x = 6 5 or x = 5 6 Hence, the required number is 5 6 or 6 5 .

The sum of a number and its reciprocal is 2 1 30 . Find the number.

Consider, the required number be x . According to the given condition, x + 1 x = 2 1 30 ⇒ ( x 2 + 1 ) x = 61 30 ⇒ 30 x 2 + 30 = 61 x ⇒ 30 x 2 - 61 x + 30 = 0 ⇒ 30 x 2 - 36 x - 25 x + 30 = 0 ⇒ 6 x ( 5 x - 6 ) - 5 ( 5 x - 6 ) = 0 ⇒ ( 5 x - 6 ) ( 6 x - 5 ) = 0 ⇒ 5 x - 6 = 0 or 6 x - 5 = 0 ⇒ x = 6 5 or x = 5 6 Hence, the required number is 5 6 or 6 5 .

MEDIUM

10th CBSE

IMPORTANT

Earn 100

The sum of a number and its reciprocal is $2 \frac{1}{30}$ . Find the number.

Important Questions on Quadratic Equations

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 29

A teacher on attempting to arrange the students for mass drill in the form of solid square found that

24

students were left. When he increased the size of the square by one student, he found that he was short of

25

students. Find the number of students.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 30

300

apples are distributed equally among a certain number of students. Had there been

10

more students, each would have received one apple less. Find the number of students.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 31

In a class test, the sum of Kamal’s marks in mathematics and English is

40

. Had he got

3

marks more in mathematics and

4

marks less in English, the product of the marks would have been

360

. Find his marks in two subjects separately.

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 32

Some students planned a picnic. The total budget for food was $₹ 2000$ . But, $5$ students failed to attend the picnic and thus the cost for food for each member increased by $₹ 20$ . How many students attended the picnic and how much did each student pay for the food?

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 33

If the price of a book is reduced by

₹ 5

, a person can buy

4

more books for

₹ 600

. Find the original price of the book.

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 34

A person on tour has

₹ 10800

for his expenses. If he extends his tour by

4

days, he has to cut down his daily expenses by

₹ 90

. Find the original duration of the tour.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 35

In a class test, the sum of the marks obtained by

P

in mathematics and science is

28

. Had he got

3

more marks in mathematics and

4

marks less in science, the product of marks obtained in the two subjects would have been

180

. Find the marks obtained by him in the two subjects separately.

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 36

A man buys a number of pens for $₹ 180$ . If he had bought $3$ more pens for the same amount, each pen would have cost him $₹ 3$ less. How many pens did he buy?

The sum of a number and its reciprocal is 2 130. Find the number.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

The sum of a number and its reciprocal is $2 \frac{1}{30}$ . Find the number.