When 6 new boys were admitted and 6 girls were left from the class the % of boys in the class increased from 60 % to 75 % . Find the original number of boys and girls in the class.

Let the number of boys be x . Let the number of girls be y . Total number of students = x + y Given, initially the percentage of boys is 60 % and when 6 boys were admitted and 6 girls were left the percentage increased to 75 % ⇒ x x + y = 60 100 . . . . ( i ) and x + 6 ( x + 6 ) + ( y - 6 ) = 75 100 . . . . ( ii ) From ( i ) , 100 x = 60 x + 60 y ⇒ 40 x - 60 y = 0 ⇒ 2 x - 3 y = 0 ⇒ 2 x = 3 y . . . ( iii ) From ( ii ) 100 x + 600 = 75 x + 75 y ⇒ 25 x - 75 y = - 600 ⇒ x - 3 y = - 24 . . . . ( iv ) Substituting value of 3 y from ( iii ) in ( iv ) , we get, x - 2 x = - 24 - x = - 24 x = 24 Substituting x value in ( iii ) , we get, 2 ( 24 ) = 3 y 48 = 3 y y = 16 Therefore, number of boys = 24 and number of girls = 16 .

EASY

10th CBSE

IMPORTANT

Earn 100

$2 kg$ of tea and $3 kg$ of sugar together costs $₹ 205$ . The price of tea rises by $20 %$ and that of sugar by $10 %$ . The same quantity of tea and sugar now costs $₹ 241.50$ . Find the original price of tea and sugar.

Important Questions on Pair Of Linear Equations In Two Variables

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 3 - Pair Of Linear Equations In Two Variables>EXERCISE>Q 44

When

2 x + 3 (9) = 205 2 x = 205 - 27 2 x = 178 x = 89

new boys were admitted and

6

girls were left from the class the

%

of boys in the class increased from

60 %

75 %

. Find the original number of boys and girls in the class.

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 3 - Pair Of Linear Equations In Two Variables>EXERCISE>Q 45

When the son will be as old as the father today their ages will add up to

126

years. When the latter was as old as the son is today, their ages added up to

38

years. Find their present ages.

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 3 - Pair Of Linear Equations In Two Variables>EXERCISE>Q 46

A lady has

25 P

and

50 P

coins in her purse. If in all she has

40

coins, totalling,

₹ 12.50

. Find the number of coins of each type she has.

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 3 - Pair Of Linear Equations In Two Variables>EXERCISE>Q 47

In an examination the number of those that passed and the number of those that failed were in the ratio.

3 : 1

. Had

8

more appeared,

6

less passed, the ratio of passed to failures would have been

2 : 1

. Find how many appeared?

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 3 - Pair Of Linear Equations In Two Variables>EXERCISE>Q 48

A boy walks to a picnic spot from his house in

6

hours, but he can travel the same distance on his cycle in

2

hours. If his average cycling speed is

7

kilometers per hour faster than his average walking speed, find his average walking speed and his average cycling speed.

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 3 - Pair Of Linear Equations In Two Variables>EXERCISE>Q 49

The width of a rectangular room is

4 / 7

of its length

x

and its perimeter is

y

. Write an equation connecting

x

and

y

. Find the length of the room when the perimeter is

4400 cm

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 3 - Pair Of Linear Equations In Two Variables>EXERCISE>Q 50

A person invested some amount at the rate of

10 %

simple interest and some other amount at the rate of

12 %

simple interest. He received yearly interest of

₹ 130

. But if he had interchanged the amounts invested, he would have received

₹ 4

more as interest. How much amount did he invest at different rates?

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 3 - Pair Of Linear Equations In Two Variables>REVISION EXERCISE>Q 1

The value of

k

for which the pair of equations

4 x + 6 y - 1 = 0

and

2 x + k y - 7 = 0

represents parallel lines is

2 kg of tea and 3 kg of sugar together costs ₹205. The price of tea rises by 20 % and that of sugar by 10%. The same quantity of tea and sugar now costs ₹241.50. Find the original price of tea and sugar.

Important Questions on Pair Of Linear Equations In Two Variables

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$2 kg$ of tea and $3 kg$ of sugar together costs $₹ 205$ . The price of tea rises by $20 %$ and that of sugar by $10 %$ . The same quantity of tea and sugar now costs $₹ 241.50$ . Find the original price of tea and sugar.