Deepak bought 3 notebooks and 2 pens for Rs. 80. His friend Ram said that price of each notebook could be Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs.5 and each pen could be for Rs. 2.50. Another friend Ajay felt that Rs2.50 for one pen was too little. It should be at least Rs. 16. Then the price of each notebook would also be Rs.16. Lohith also bought the same types of notebooks and pens as Aditya. He paid 110 for 4 notebooks and 3 pens. Later, Deepak guess the cost of one pen is Rs. 10 and Lohith guess the cost of one notebook is Rs. 30.
(i)Form the pair of linear equations in two variables from this situation by taking cost of one notebook as Rs. x and cost of one pen as Rs. y.
(a) 3x + 2y = 80 and 4x + 3y = 110
(b) 2x + 3y = 80 and 3x + 4y = 110
(c) x + y = 80 and x + y = 11
(d) 3x + 2y = 110 and 4x + 3y = 80
(ii) Find the cost of one notebook.
(a) Rs. 20 (b) Rs. 10 (c) Rs. 5 (d) Rs. 15
(iii) Find the cost of one pen.
(a)Rs. 20 (b) Rs. 10 (c) Rs. 5 (d) Rs. 15
(iv) Find the total cost if they will purchase the same type of 15 notebooks and 12 pens. (a) Rs. 400 (b) Rs. 350 (c) Rs. 450 (d) Rs. 420
(v) Find whose estimation is correct in the given statement.
(a) Deepak (b) Lohith (c) Ram (d) Ajay
Answers
Answer:
(i) (a) (ii) (a) (iii) (b) (iv) (d) (v) (a)
Step-by-step explanation:
(ii) 3x + 2y = 80 . . . . .(1)
4x + 3y = 110 . . . . . .(2)
(1) x 3 - (2) x 2
9x + 6 y = 240
8x + 6 y = 220
x = 20 Rs cost of one note book
From (1) 2y = 80 - 60 = 20 ⇒ y = 10 Rs. cost of one pen
iv) 15x + 12y = 15 x 20 + 12 x 10 = 300 + 120 = 420 Rs
1)(a) 3x + 2y = 80 and 4x + 3y = 110.
2) (a) Rs-20
3) (b) Rs-10
4) (d) Rs-420
5) Deepak
Step-by-step explanation:
1) cost of Notebook = x
cost of Pen = y
As per Given information:
(i) 3 Notebooks + 2 pens = rs 80
3x + 24 = 80
similarly,
4 Notebooks + 3 pens = rs-110
4x +34 = 110.
3x + 2y = 80 and 4x + 3y = 110.
2) cost of Notebook (x)
To find x
solve 3x + 2y = 80 → (1)
4x + 3y = 110 → (2)
by eliminating y
1 × 3 9x+6y=240
2 × 2
(-) (-)
therefore The cost of Notebook is rs. 20
(iii) Costs of pens (y)
To Find y eliminate x to substitute x = 20
in 3x + 2y = 80 (or)
4x + 3y = 110
x = 20 in 3x + 2y = 80
3(20)+2y = 80
60 + 2y = 80
2y = 80
y = 20/2
y=10
The cost of pen = 10
(iv) 3 Notebooks (x = 15) and Pens (y = 12)
Find cost = ?
15x+12y = ?
[x=20] [y=10] = 15 (20) + 12 (10)
= 300 + 120
= Rs-420
(v) Ram said that price of each notebook could be Rs-25.
Ajay felt that Rs-2.50 for one pen was too little. It should be at least Rs-16 Deepak guess the cost of one pen is Rs-10 and Lohith guess the cost of one notebook is Rs-30
Therefore, estimation of Deepak is correct