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# RD Sharma Solutions: Exercise 3.6 - Pair of Linear Equations in Two Variables Notes | EduRev

## Class 10 : RD Sharma Solutions: Exercise 3.6 - Pair of Linear Equations in Two Variables Notes | EduRev

``` Page 1

Exercise 3.6

1. 5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of
1 pen and 1 pencil.
Sol:
Let the cost of a pen be Rs x and that of a pencil be Rs y. Then,
? ?
? ?
5 6 9 .......
3 2 5 ......
x y i
and x y ii
? ?
??

Multiplying equation (i) by 2 and equation (ii) by 6, we get
? ?
? ?
10 12 18 ......
18 12 30 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iii) by equation (iv), we get
18 10 12 12 30 18
8 12
12 3
1.5
82
x x y y
x
x
? ? ? ? ?
? ?
? ? ? ?

Substituting 1.5 x ? in equation (i), we get
5 1.5 6 9
7.5 6 9
6 9 7.5
6 1.5
1.5 1
0.25
64
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ? ?

Hence, cost of one pen 1.50 Rs ? and cost of one pencil 0.25 Rs ?

Page 2

Exercise 3.6

1. 5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of
1 pen and 1 pencil.
Sol:
Let the cost of a pen be Rs x and that of a pencil be Rs y. Then,
? ?
? ?
5 6 9 .......
3 2 5 ......
x y i
and x y ii
? ?
??

Multiplying equation (i) by 2 and equation (ii) by 6, we get
? ?
? ?
10 12 18 ......
18 12 30 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iii) by equation (iv), we get
18 10 12 12 30 18
8 12
12 3
1.5
82
x x y y
x
x
? ? ? ? ?
? ?
? ? ? ?

Substituting 1.5 x ? in equation (i), we get
5 1.5 6 9
7.5 6 9
6 9 7.5
6 1.5
1.5 1
0.25
64
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ? ?

Hence, cost of one pen 1.50 Rs ? and cost of one pencil 0.25 Rs ?

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.
Sol:
Let the cost of a audio cassette beRs x and that of a video cassette be . Rs y Then,
? ?
? ?
7 3 1110 ....
5 4 1350 ....
x y i
and x y ii
??
??

Multiplying equation (i) by 4 and equation (ii) by 3, we get
? ?
? ?
28 12 4440 ......
15 12 4050 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iv) from equation (iii), we get
28 15 12 12 4440 4050
13 390
x x y y
x
? ? ? ? ?
? ?

390
30
13
x ? ? ?
Substituting equation (iv) from equation (iii), we get
28 15 12 12 4440 4050 x x y y ? ? ? ? ?
13 390 x ? ?
390
30
13
x ? ? ?
Substituting 30 x ? in equation (i), w get
7 30 3 1110
210 3 1110
3 1110 210
3 900
900
300
3
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ?

Hence, cost of one audio cassette 30 Rs ? and cost of one video cassette 300 Rs ?

3. Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and
5 less pens, then nuimber of pencils would become 4 times the number of pens. Find the
original number of pens and pencils.
Sol:
Let the number of pens be x and that of pencil be y. then,
? ? ? ?
40 .......( )
5 4 5
x y i
and y x
??
? ? ?

Page 3

Exercise 3.6

1. 5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of
1 pen and 1 pencil.
Sol:
Let the cost of a pen be Rs x and that of a pencil be Rs y. Then,
? ?
? ?
5 6 9 .......
3 2 5 ......
x y i
and x y ii
? ?
??

Multiplying equation (i) by 2 and equation (ii) by 6, we get
? ?
? ?
10 12 18 ......
18 12 30 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iii) by equation (iv), we get
18 10 12 12 30 18
8 12
12 3
1.5
82
x x y y
x
x
? ? ? ? ?
? ?
? ? ? ?

Substituting 1.5 x ? in equation (i), we get
5 1.5 6 9
7.5 6 9
6 9 7.5
6 1.5
1.5 1
0.25
64
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ? ?

Hence, cost of one pen 1.50 Rs ? and cost of one pencil 0.25 Rs ?

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.
Sol:
Let the cost of a audio cassette beRs x and that of a video cassette be . Rs y Then,
? ?
? ?
7 3 1110 ....
5 4 1350 ....
x y i
and x y ii
??
??

Multiplying equation (i) by 4 and equation (ii) by 3, we get
? ?
? ?
28 12 4440 ......
15 12 4050 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iv) from equation (iii), we get
28 15 12 12 4440 4050
13 390
x x y y
x
? ? ? ? ?
? ?

390
30
13
x ? ? ?
Substituting equation (iv) from equation (iii), we get
28 15 12 12 4440 4050 x x y y ? ? ? ? ?
13 390 x ? ?
390
30
13
x ? ? ?
Substituting 30 x ? in equation (i), w get
7 30 3 1110
210 3 1110
3 1110 210
3 900
900
300
3
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ?

Hence, cost of one audio cassette 30 Rs ? and cost of one video cassette 300 Rs ?

3. Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and
5 less pens, then nuimber of pencils would become 4 times the number of pens. Find the
original number of pens and pencils.
Sol:
Let the number of pens be x and that of pencil be y. then,
? ? ? ?
40 .......( )
5 4 5
x y i
and y x
??
? ? ?

? ?
5 4 20
5 20 4
4 25 ......
yx
xy
x y ii
? ? ? ?
? ? ? ?
? ? ?

Adding equation (i) and equation (ii), we get
4 40 25
5 65
65
13
5
xx
x
x
? ? ?
??
? ? ?

Putting 13 x ? in equation (i), we get
13 40
40 13 27
y
y
? ?
? ? ? ?

Hence, Reena has13pens 27 pencils.

4. 4 tables and 3 chairs, together, cost Rs 2,250 and 3 tables and 4 chairs cost Rs 1950. Find
the cost of 2 chairs and 1 table.
Sol:
Let the cost of a table be Rsx and that of a chairs be . Rs y Then,
? ? 4 3 2,250 .....
, 3 4 1950 .....( )
x y i
and x y ii
? ?
? ?

Multiplying equation (i) by 4 and equation (ii) by 3, we get
? ?
16 12 9000 ......( )
9 12 5850 .......
x y iii
x y iv
??
??

Subtracting equation (iv) by equation (iii), we get
16 9 9000 5850
7 3150
3150
450
7
xx
x
x
? ? ?
??
? ? ?

Putting 450 x ? in equation (i), we get
4 450 3 2,250
1800 3 2250
3 2250 1800
3 450
450
150
3
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ?

2 2 150 300 y ? ? ? ?
Cost of 2 chairs   300 Rs ? and cost of 1 table   450 Rs ?
?The cost of 2 chairs and 1 table 300 450 750 Rs ? ? ?
Page 4

Exercise 3.6

1. 5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of
1 pen and 1 pencil.
Sol:
Let the cost of a pen be Rs x and that of a pencil be Rs y. Then,
? ?
? ?
5 6 9 .......
3 2 5 ......
x y i
and x y ii
? ?
??

Multiplying equation (i) by 2 and equation (ii) by 6, we get
? ?
? ?
10 12 18 ......
18 12 30 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iii) by equation (iv), we get
18 10 12 12 30 18
8 12
12 3
1.5
82
x x y y
x
x
? ? ? ? ?
? ?
? ? ? ?

Substituting 1.5 x ? in equation (i), we get
5 1.5 6 9
7.5 6 9
6 9 7.5
6 1.5
1.5 1
0.25
64
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ? ?

Hence, cost of one pen 1.50 Rs ? and cost of one pencil 0.25 Rs ?

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.
Sol:
Let the cost of a audio cassette beRs x and that of a video cassette be . Rs y Then,
? ?
? ?
7 3 1110 ....
5 4 1350 ....
x y i
and x y ii
??
??

Multiplying equation (i) by 4 and equation (ii) by 3, we get
? ?
? ?
28 12 4440 ......
15 12 4050 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iv) from equation (iii), we get
28 15 12 12 4440 4050
13 390
x x y y
x
? ? ? ? ?
? ?

390
30
13
x ? ? ?
Substituting equation (iv) from equation (iii), we get
28 15 12 12 4440 4050 x x y y ? ? ? ? ?
13 390 x ? ?
390
30
13
x ? ? ?
Substituting 30 x ? in equation (i), w get
7 30 3 1110
210 3 1110
3 1110 210
3 900
900
300
3
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ?

Hence, cost of one audio cassette 30 Rs ? and cost of one video cassette 300 Rs ?

3. Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and
5 less pens, then nuimber of pencils would become 4 times the number of pens. Find the
original number of pens and pencils.
Sol:
Let the number of pens be x and that of pencil be y. then,
? ? ? ?
40 .......( )
5 4 5
x y i
and y x
??
? ? ?

? ?
5 4 20
5 20 4
4 25 ......
yx
xy
x y ii
? ? ? ?
? ? ? ?
? ? ?

Adding equation (i) and equation (ii), we get
4 40 25
5 65
65
13
5
xx
x
x
? ? ?
??
? ? ?

Putting 13 x ? in equation (i), we get
13 40
40 13 27
y
y
? ?
? ? ? ?

Hence, Reena has13pens 27 pencils.

4. 4 tables and 3 chairs, together, cost Rs 2,250 and 3 tables and 4 chairs cost Rs 1950. Find
the cost of 2 chairs and 1 table.
Sol:
Let the cost of a table be Rsx and that of a chairs be . Rs y Then,
? ? 4 3 2,250 .....
, 3 4 1950 .....( )
x y i
and x y ii
? ?
? ?

Multiplying equation (i) by 4 and equation (ii) by 3, we get
? ?
16 12 9000 ......( )
9 12 5850 .......
x y iii
x y iv
??
??

Subtracting equation (iv) by equation (iii), we get
16 9 9000 5850
7 3150
3150
450
7
xx
x
x
? ? ?
??
? ? ?

Putting 450 x ? in equation (i), we get
4 450 3 2,250
1800 3 2250
3 2250 1800
3 450
450
150
3
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ?

2 2 150 300 y ? ? ? ?
Cost of 2 chairs   300 Rs ? and cost of 1 table   450 Rs ?
?The cost of 2 chairs and 1 table 300 450 750 Rs ? ? ?

5. 3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost R 324.
Find the total cost of 1 bag and 10 pens.
Sol:
Let the cost of a bag be Rs x and that of a pen be Rs y . Then,
? ?
? ?
3 4 257 .....
, 4 3 324 .....
x y i
and x y ii
??
? ?

Multiplying equation (i) by 3 and equation (ii) by 4, we get
? ?
? ?
9 12 770 ....
16 12 1296 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iii) by equation (iv), we get
16 9 1296 771
7 525
525
75
7
xx
x
x
? ? ?
? ?
? ? ?

Cost of a bag 75 Rs ?
Putting 75 x ? in equation (i), we get
3 75 4 257
225 4 257
4 257 225
4 32
32
8
4
y
y
y
y
y
? ? ?
? ? ?
? ? ?
? ?
? ? ?

? Cost of a pen 8 Rs ?
? Cost of 10 pens 8 10 80 Rs ? ? ?
Hence, the total cost of 1 bag and 10 pens 75 80 155. Rs ? ? ?

6. 5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens together cost Rs 77.
Find the total cost of 1 book and 2 pens.
Sol:
Let the cost of a book be Rs x and that of a pen be Rs y. Then,
? ?
? ?
5 7 79 .....
, 7 5 77 ....
x y i
and x y ii
??
? ?

Multiplying equation (i) by 5 and equation (ii) by 7, we get
? ?
? ?
25 35 395 ......
49 35 539 .......
y iii
x y iv
? ?
? ?

Page 5

Exercise 3.6

1. 5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of
1 pen and 1 pencil.
Sol:
Let the cost of a pen be Rs x and that of a pencil be Rs y. Then,
? ?
? ?
5 6 9 .......
3 2 5 ......
x y i
and x y ii
? ?
??

Multiplying equation (i) by 2 and equation (ii) by 6, we get
? ?
? ?
10 12 18 ......
18 12 30 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iii) by equation (iv), we get
18 10 12 12 30 18
8 12
12 3
1.5
82
x x y y
x
x
? ? ? ? ?
? ?
? ? ? ?

Substituting 1.5 x ? in equation (i), we get
5 1.5 6 9
7.5 6 9
6 9 7.5
6 1.5
1.5 1
0.25
64
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ? ?

Hence, cost of one pen 1.50 Rs ? and cost of one pencil 0.25 Rs ?

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.
Sol:
Let the cost of a audio cassette beRs x and that of a video cassette be . Rs y Then,
? ?
? ?
7 3 1110 ....
5 4 1350 ....
x y i
and x y ii
??
??

Multiplying equation (i) by 4 and equation (ii) by 3, we get
? ?
? ?
28 12 4440 ......
15 12 4050 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iv) from equation (iii), we get
28 15 12 12 4440 4050
13 390
x x y y
x
? ? ? ? ?
? ?

390
30
13
x ? ? ?
Substituting equation (iv) from equation (iii), we get
28 15 12 12 4440 4050 x x y y ? ? ? ? ?
13 390 x ? ?
390
30
13
x ? ? ?
Substituting 30 x ? in equation (i), w get
7 30 3 1110
210 3 1110
3 1110 210
3 900
900
300
3
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ?

Hence, cost of one audio cassette 30 Rs ? and cost of one video cassette 300 Rs ?

3. Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and
5 less pens, then nuimber of pencils would become 4 times the number of pens. Find the
original number of pens and pencils.
Sol:
Let the number of pens be x and that of pencil be y. then,
? ? ? ?
40 .......( )
5 4 5
x y i
and y x
??
? ? ?

? ?
5 4 20
5 20 4
4 25 ......
yx
xy
x y ii
? ? ? ?
? ? ? ?
? ? ?

Adding equation (i) and equation (ii), we get
4 40 25
5 65
65
13
5
xx
x
x
? ? ?
??
? ? ?

Putting 13 x ? in equation (i), we get
13 40
40 13 27
y
y
? ?
? ? ? ?

Hence, Reena has13pens 27 pencils.

4. 4 tables and 3 chairs, together, cost Rs 2,250 and 3 tables and 4 chairs cost Rs 1950. Find
the cost of 2 chairs and 1 table.
Sol:
Let the cost of a table be Rsx and that of a chairs be . Rs y Then,
? ? 4 3 2,250 .....
, 3 4 1950 .....( )
x y i
and x y ii
? ?
? ?

Multiplying equation (i) by 4 and equation (ii) by 3, we get
? ?
16 12 9000 ......( )
9 12 5850 .......
x y iii
x y iv
??
??

Subtracting equation (iv) by equation (iii), we get
16 9 9000 5850
7 3150
3150
450
7
xx
x
x
? ? ?
??
? ? ?

Putting 450 x ? in equation (i), we get
4 450 3 2,250
1800 3 2250
3 2250 1800
3 450
450
150
3
y
y
y
y
y
? ? ?
? ? ?
? ? ?
??
? ? ?

2 2 150 300 y ? ? ? ?
Cost of 2 chairs   300 Rs ? and cost of 1 table   450 Rs ?
?The cost of 2 chairs and 1 table 300 450 750 Rs ? ? ?

5. 3 bags and 4 pens together cost Rs 257 whereas 4 bags and 3 pens together cost R 324.
Find the total cost of 1 bag and 10 pens.
Sol:
Let the cost of a bag be Rs x and that of a pen be Rs y . Then,
? ?
? ?
3 4 257 .....
, 4 3 324 .....
x y i
and x y ii
??
? ?

Multiplying equation (i) by 3 and equation (ii) by 4, we get
? ?
? ?
9 12 770 ....
16 12 1296 ......
x y iii
x y iv
? ?
? ?

Subtracting equation (iii) by equation (iv), we get
16 9 1296 771
7 525
525
75
7
xx
x
x
? ? ?
? ?
? ? ?

Cost of a bag 75 Rs ?
Putting 75 x ? in equation (i), we get
3 75 4 257
225 4 257
4 257 225
4 32
32
8
4
y
y
y
y
y
? ? ?
? ? ?
? ? ?
? ?
? ? ?

? Cost of a pen 8 Rs ?
? Cost of 10 pens 8 10 80 Rs ? ? ?
Hence, the total cost of 1 bag and 10 pens 75 80 155. Rs ? ? ?

6. 5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens together cost Rs 77.
Find the total cost of 1 book and 2 pens.
Sol:
Let the cost of a book be Rs x and that of a pen be Rs y. Then,
? ?
? ?
5 7 79 .....
, 7 5 77 ....
x y i
and x y ii
??
? ?

Multiplying equation (i) by 5 and equation (ii) by 7, we get
? ?
? ?
25 35 395 ......
49 35 539 .......
y iii
x y iv
? ?
? ?

Subtracting equation (iii) by equation (iv), we get
49 25 539 395
24 144
144
6
24
xx
x
x
? ? ?
??
? ? ?

? Cost of a book 6 Rs ?
Putting 6 x ? in equation (i), we get
5 6 7 79
30 7 79
7 79 30
7 49
79
7
7
y
y
y
y
y
? ? ?
? ? ?
? ? ?
? ?
? ? ?

? Cost of a pen 7 Rs ?
? Cost of 2 pens 2 7 14 Rs ? ? ?
Hence, the total cost of 1 book and 2 pens 6 14 20 Rs ? ? ?

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?
Sol:
Suppose A has x mangoes and B has y mangoes
According to the given conditions, we have
? ?
? ?
30 2 30
30 2 60
2 60 30
2 90 ....
xy
xy
xy
x y i
? ? ?
? ? ? ?
? ? ? ? ?
? ? ? ?

And, ? ? 10 3 10 yx ? ? ?
? ?
10 3 30
10 30 3
3 40 ....
yx
xy
x y ii
? ? ? ?
? ? ? ?
? ? ? ?

Multiplying equation (i) by 3 and equation (ii) by 1, we get
? ?
? ?
3 6 270 .....
3 40 ......
x y iii
x y iv
? ? ?
??

Subtracting equation (iv) by equation (iii), we get
```
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