Question

Question No. 1 of 15 1 Marks
For an painting exhibition, Ruhi bought 5 paint brushes, 4 drawing book and 12 water
colors packet for Rs. 314. Chandu bought 7 drawing book, 21 water colors packet and 6
paint brushes for Rs. 522. Find the cost of a paint brush, if all the water colors packet
cost the same.
O Rs 30
O Rs 20
O Rs 50
O Rs 10
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Answer 1

The cost of a paint brush, if all the water colors packet cost the same is Rs. 10

Given : For an painting exhibition, Ruhi bought 5 paint brushes, 4 drawing book and 12 water colors packet for Rs. 314. Chandu bought 7 drawing book, 21 water colors packet and 6 paint brushes for Rs. 522

To find : The cost of a paint brush, if all the water colors packet cost the same

Rs 30

Rs 20

Rs 50

Rs 10

Solution :

Let

The cost of a paint brush = Rs. P

The cost of a drawing book = Rs. D

The cost of a water colors packet = Rs. W

By the given condition 1

5P + 4D + 12W = 314 - - - - - (1)

By the given condition 2

6P + 7D + 21W = 522 - - - - - - (2)

Multiplying both sides of Equation 1 and Equation 2 by 7 and 4 respectively we get

35P + 28D + 84W = 2198 - - - - - (3)

24P + 28W + 84W = 2088 - - - - - (4)

Equation 3 - Equation 4 gives

11P = 110

⇒ P = 10

Hence cost of a paint brush = Rs. 10

So the correct option is Rs. 10

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Answer 2

As per the data given in the above question.

we have to find the cost of brushes .

Given ,

• Ruhi bought

5 paint brushes +4 drawing book + 12 water

colors packet = Rs. 314 .........(i)

• Chandu bought

7 drawing book+21 water colors packet+ 6

paint brushes= Rs. 522.........(ii)

• water color cost is same for both Ruhi and chandu

Now ,

Let the cost of a paint brush = ₹ x

Let the cost of a paint brush = ₹ xLet the cost of a drawing book =₹ y

Let the cost of a paint brush = ₹ xLet the cost of a drawing book =₹ yLet the cost of a water colors = ₹ z

From given condition, equation (i)

$5x+4y+12z=314. .........(iii)$

From given condition , equation (ii)

$6x+7y+21z=522. ..........(iv)$

We have to apply elimination method,

Multiply equation (iii) by 7 and equation (iv) by 4 respectively we get ,

$35x+28y+84z=2198. .......(v)$

and

$24x+28y+84z=2088. .......(vi)$

Subtract equation (vi) from (v) , we get

$35x+28y+84z-(24x+28y+84z)=2198-2088$

$35x+28y+84z-24x-28y-84z=2198-2088$

y and z values cancel each other due to postive and negative values ,

$35x - 24x = 110$

$11x = 110$

Shift the 11 toward 110 in division,

$x = \frac{110}{11}$

$x = 10$

The cost of paint brush is ₹10.

Hence ,

option (d) ₹10 is correct .

Project code #SPJ2