A shopkeeper sold an article at 20 % discount and made a loss of Rs 90. If he had sold it at 5 % discount, he would have gained Rs 90. Find the cost price and the
marked price of the article.

The cost price of the article is Rs 1050

The marked price of the article Rs 1200

Step-by-step explanation:

The given discount on the article = 20%

The amount loss  = Rs 90

With a discount of 5% the amount gained = Rs 90

Let the cost price of the article = X

Let the marked price of the article = Y

Therefore, we have;

(1 - 0.2) × Y = X - Rs 90

(1 - 0.5) × Y = X + Rs 90

Which gives;

0.8·Y = X - Rs 90 (1)

0.95·Y = X + Rs 90(2)

Subtracting equation (1) from equation (2), we have;

0.95·Y-0.8·Y = X + Rs 90 - (X - Rs 90) = X - X + Rs 90 + Rs 90 = Rs 180

0.15·Y = Rs 180

Y = Rs 180/0.15 = Rs 1200

Therefor, the marked price of the article = Rs 1200

From;

0.8·Y = X - Rs 90, we have;

0.8×Rs 1200 = X - Rs 90

X = 0.8× 1200 + 90 = Rs 1050

Therefore, the cost price of the article = Rs 1050.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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