Could u please answer this question. A piece of cloth costs Rs 200.If the cloth was 5m Longer and each metre of cloth costs Rs 2 less.How long is the piece and what is the orginal rate per metre.
Answers
Let the length of the cloth be ‘x’ and cost of cloth per
meters be Rs y
Then, xy = 200
and, y = 200/x → (1)
Given that, if the piece were 5 m longer, and each meter of
cloth costs Rs 2 less
So, we get,
⇒ (x+5)(y – 2) = 200
⇒xy – 2x + 5y – 10 = 200
Putting ‘y’ value from (1),
We get, 200 – 2x + 5(200/x) – 10 = 200
⇒ (1000/x) – 2x = 200 – 190
⇒ 1000 – 2x² = 10x
⇒ 500 – x² = 5x
⇒ x²+5x – 500 = 0
⇒ x² + 25x – 20x – 500 =0
⇒ x(x+25) – 20(x+25) = 0
⇒ (x – 20) (x + 25) = 0
∴ x = 20 or x = -25
But length cannot be negative, therefore x = 20 m
Thus, y = 200/x
= 200/20
= 10
Therefore, the length of the cloth be 20 m and cost of cloth
per meter is Rs 20.
There's an alternate method too:
Let the length of the original piece be x
Now, it's price = Rs.200
So, Price per m = 200/x .....(1)
Now, if the cloth was 5 m longer, its length = x+5
And, Price per m would be 200/x+5 .....(2)
(As total price is unchanged)
Or, Price per m would be Rs.2 less than the original one i.e.
200/x -2 .....(3)
Equating (2) & (3),
We get, 200/x+5 = 200/x - 2
⇒ 200/x+5 = 200-2x/x
⇒ 200x/x+5 = 200 -2x
⇒ 200x = (x+5)(200-2x)
⇒ 200x = 200x -2x² +1000 -10x
Cancelling 200x from both sides,
We get, -2x² -10x +1000 = 0
Solving the quadratic equation, we'll get the answer. I'm not presenting it again as I have done it in the first method.
Now, Substituting values in the formula,
So, Root 1 = 10 + √ [10² - 4(- 2) (1000) ] / -4
= 10 + 90 / -4
= 100 / -4
= -25
And, Root 2 = 10 -√ [10² - 4 (-2) (1000) ] / -4
= 10 - 90 / -4
= -80 / -4
= 20
Now, the length of the original piece cannot be negative.
So, the length of original piece is 20 m (Root 2)
And, original rate = 200/x
= 200/20
= 10 Rs./m
Hope This Helps :)