RD Sharma Solutions Chapter 3 Pair of Linear Equation in Two Variables Exercise 3.6 Class 10 Maths
Chapter Name  RD Sharma Chapter 3 Pair of Linear Equation in Two Variables 
Book Name  RD Sharma Mathematics for Class 10 
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Related Study  NCERT Solutions for Class 10 Maths 
Exercise 3.6 Solutions
Let the cost of a pen be Rs x and that of a pencil be Rs y. Then,
5x + 6y = 9 ...(i)
and 3x + 2y = 5 ...(ii)
Multiplying equation (i) by 2 and equation (ii) by 6, we get
10x + 12y = 18 ...(iii)
18x + 12y = 30 ...(iv)
Subtracting equation (iii) by equation (iv), we get
18x  10x + 12y  12y = 30  18
2. 7 audio cassettes and 3 video cassettes cost Rs 1110, while 5 audio cassettes and 4 video cassettes cost Rs 1350. Find the cost of an audio cassette and a video cassette.
Let the cost of a audio cassette be Rs x and that of a video casette be Rs y. Then,
7x + 3y = 1110 ...(i)
and 5x + 4y = 1350 ...(ii)
Multiplying equation (i) by 4 and equation (ii) by 3, we get
28x + 12y = 4440 ...(iii)
15x + 12y = 4050 ...(iv)
Subtracting equation (iv) from equation (iii), we get
28x  15x + 12y  12y = 4440  4050
x + y = 40 ...(i)
and (y +5) = 4(x  5)
Let the cost of a table be Rs x and that of a chairs be Rs y. Then,
4x + 3y = 2,250 ...(i)
and, 3x + 4y = 1950 ...(ii)
Multiplying equation (i) by 4 and equation (ii) by 3, we get
16x + 12y = 9000 ...(iii)
9x + 12y = 5850 ...(iv)
Subtracting equation (iv) by equation (iii), we get
16x  9x = 9000  5850
5. 3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost Rs 324. Find the total cost of 1 bag and 10 pens.
Let the cost of a bag be Rs x and that of a pen be Rs y. Then,
3x + 4y = 257 ...(i)
and, 4x + 3y = 324 ...(ii)
Multiplying equation (i) by 3 and equation (ii) by 4, we get
9x + 12y = 770 ...(iii)
16x + 12y = 1296 ...(iv)
Subtracting equation (iii) by equation (iv), we get
16x  9x = 1296  771
Let the cost of a book be Rs x and that of a pen be Rs y. Then,
5x + 7y = 79 ...(i)
and 7x + 5y = 77 ...(ii)
Multiplying equation (i) by 5 and equation (ii) by 7, we get
25x + 35y = 395 ...(iii)
49x + 35y = 539 ...(iv)
Subtracting equation (iii) by equation (iv), we get
49x  25x = 539  395
7. A and B each have a certain number of mangoes. A says to B, " if you give 30 of your mangoes. I will have twice as many as left with you." B replies, " if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
Suppose A has x mangoes and B has y mangoes
According to the given conditions, we have
Let the price of a T.V. be Rs x and that of a fridge be Rs y. Then, we have
According to the given information
Hence, the cost of a bat is Rs 500 and that of a ball is Rs 50.
Concept Insight: Cost of bats and balls needs to be found so the cost of a ball and bat will be taken as the variables. Applying the conditions of total cost of bats and balls algebraic equations will be obtained. The pair of equations can then be solved by suitable substitution.
Let the money with the first person and second person be Rs x and Rs y respectively.
According to the question
Le the fixed charge for first three days and each day charge thereafter be Rs x and Rs y respectively.
According to the question,