Question

17.Dipesh bought 3 notebooks and 2 pens for Rs. 80. His friend Ramesh 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 Amar felt that Rs. 2.50
for one pen was too little. It should be at least Rs. 16. Then the price of each notebook
would also be Rs.16. Lokesh also bought the same types of notebooks and pens as Dipesh.
He paid 110 for 4 notebooks and 3 pens
Let the cost of one notebook be x and that of pen be y .

( I ) Which of the following set describe the given problem ?
(a) 2x + 3 y = 80 and 3x + 4 y = 110
(b) 3x + 2 y = 80 and 4x + 3 y = 110
(c) 2x + 3 y = 80 and 4x + 3 y = 110 (d) 3x + 2 y = 80 and 3x + 4 y = 110

( II ) Whether the estimation of Ramesh and Amar is applicable for Lokesh?
( a) Ramesh’s estimation is wrong but Amar’s estimation is correct.
(b) Ramesh’s estimation is correct but Amar’s estimation is wrong.
(c) Both estimation are correct.
(d) Ramesh’s estimation is wrong but Amar’s estimation is also wrong.

( III ) What is the exact cost of the notebook?
(a) Rs 10 (b) Rs 20 (c) Rs 16 (d) Rs 24
( IV ) What is the exact cost of the pen?
(a) Rs 10 (b) Rs 20 (c) Rs 16 (d) Rs 24
( V) What is the total cost if they will purchase the same type of 15 notebooks and 12 pens.
(a) Rs 410 (b) Rs 200 (c) Rs 420 (d) Rs 240​

Answer 1

SOLUTION

Here it is given that cost of one notebook be x and that of pen be y .

Then cost of 3 notebooks and 2 pens

$= \sf{3x + 2y}$

Again cost of 4 notebooks and 3 pens

$\sf{ = 4x + 3y}$

So by the given condition

$\sf{3x + 2y = 80 \: \: \: ........(1)}$

$\sf{4x + 3y = 110 \: \: \: .......(2)}$

Which is set of equations to describe the given problem

Hence the set describe the given problem is

(b) 3x + 2 y = 80 and 4x + 3 y = 110

Now we solve from x and y

Multiplying Equation (1) by 3 and equation (2) by 2 we get

$\sf{9x + 6y = 240}$

$\sf{8x + 6y = 220}$

On substraction we get x = 20

From Equation (1) we get y = 10

Hence cost of one notebook is 20 and that of pen be 10

Ramesh said that price of each notebook could be Rs. 25

So Ramesh's estimation is wrong

Amar felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16

So Amar's estimation is wrong

( II ) Whether the estimation of Ramesh and Amar is applicable for Lokesh

(d) Ramesh’s estimation is wrong but Amar’s estimation is also wrong.

Solving Equation (1) & Equation (2)

we get x = 20 & y = 10

( III ) The exact cost of the notebook

(b) Rs 20

( IV ) The exact cost of the pen

(a) Rs 10

The cost of 15 notebooks

= Rs ( 15 × 20 )

= Rs 300

The cost of 12 pens

= Rs ( 12 × 10 )

= Rs 120

Hence total cost

= Rs ( 300 + 120 )

= Rs 420

The total cost if they will purchase the same type of 15 notebooks and 12 pens.

(c) Rs 420

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Answer 2

Answer:

(I) option b

(ii) option c

(iii) option b

(iv) option a

(v) option c