A railway half ticket costs half the full fare and the reservation charge is the some on half ticket as on full ticket. One reserved first class ticket from Mumbai to Delhi costs ₹ 4150 while one full and one half reserved first class ticket cost ₹ 6255 . What is the basic first class full fare and what is the reservation charge?

Let the basic first class full fare be ₹ x and the reservation charge be ₹ y . Case 1: One reservation first class full ticket cost ₹ 4 , 150 x + y = 4150 … … … ( i ) Case 2: One full and one half reserved first class tickets cost ₹ 6 , 255 ( x + y ) + ( 1 2 x + y ) = 6255 ⇒ 3 x + 4 y = 12510 … … … ( ii ) Substituting y = 4150 - x in i i , we get ⇒ 3 x + 4 ( 4150 - x ) = 12510 ⇒ 3 x - 4 x + 16600 = 12510 ⇒ x = 16600 - 12510 = 4090 Now, substituting x = 4090 in i , we have ⇒ 4090 + y = 4150 ⇒ y = 4150 - 4090 = 60 Hence, cost of basic first class full fare is ₹ 4 , 090 and reservation charge is ₹ 60 .

HARD

10th CBSE

IMPORTANT

Earn 100

The area of a rectangle gets reduced by $67$ square meters, when its length is increased by $3 m$ and the breadth is decreased by $4 m$ . If the length is reduced by $1 m$ and breadth is increased by $4 m$ , the area is increased by $89$ square meters. Find the dimensions of the rectangle.

Important Questions on Linear Equations in Two Variables

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 3 - Linear Equations in Two Variables>Exercise 3E>Q 41

A railway half ticket costs half the full fare and the reservation charge is the some on half ticket as on full ticket. One reserved first class ticket from Mumbai to Delhi costs

(i i)

while one full and one half reserved first class ticket cost

₹ 6255

. What is the basic first class full fare and what is the reservation charge?

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 3 - Linear Equations in Two Variables>Exercise 3E>Q 42

Five years hence, a man’s age will be three times the sum of the age of his son. Five years ago, the man was seven times as old as his son. Find their present ages

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 3 - Linear Equations in Two Variables>Exercise 3E>Q 43

Two years ago, a man was five times as old as his son. Two years later, his age will be

8

more than three times the ago of the son. Find the present ages of the man.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 3 - Linear Equations in Two Variables>Exercise 3E>Q 44

If twice the son’s age in years is added to the father’s age, the sum is

70

. But, if twice the father’s age is added to the son’s age, the sum is

95

. Find the ages of father and son.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 3 - Linear Equations in Two Variables>Exercise 3E>Q 45

The present age of a woman is

3

years more than three times the age of her daughter. Three years hence, the woman’s age will be

10

years more than twice the age of her daughter. Find their present ages.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 3 - Linear Equations in Two Variables>Exercise 3E>Q 46

On selling a tea-set at

5 %

loss and a lemon-set at

15 %

gain, a crockery seller gains

₹ 7

. If he sells the tea-set at

5 %

gain and the lemon-set at

10 %

gain, he gains

₹ 13

. Find the actual price of each of the tea-set and that of the lemon-set.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 3 - Linear Equations in Two Variables>Exercise 3E>Q 47

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Mona paid

₹ 27

for a book kept for

7

days, while Tanvy paid

₹ 21

for the book she kept for

5

days. Find the fixed charge and the charge for each extra day

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 3 - Linear Equations in Two Variables>Exercise 3E>Q 48

A chemist has one solution containing

50 %

acid and a second one containing

25 %

acid. How much of each should be used to make

10

litres of a

40 %

acid solution?

The area of a rectangle gets reduced by 67 square meters, when its length is increased by 3 m and the breadth is decreased by 4 m. If the length is reduced by 1 m and breadth is increased by 4 m, the area is increased by 89 square meters. Find the dimensions of the rectangle.

Important Questions on Linear Equations in Two Variables

Learn and Prepare for any exam you want !

The area of a rectangle gets reduced by $67$ square meters, when its length is increased by $3 m$ and the breadth is decreased by $4 m$ . If the length is reduced by $1 m$ and breadth is increased by $4 m$ , the area is increased by $89$ square meters. Find the dimensions of the rectangle.