A shopkeeper charges sales tax of X% up to Rs 2000 and above it he charges Y%. A customer pays total tax of Rs 320, when he purchased the goods worth Rs 6000 and he also pay's the total tax of rupees Rs 680 for the goods worth Rs 12000. Find the value of (X - Y).?

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A shopkeeper charges sales tax of X% up to Rs 2000 and above it he cha...

Solution:

Let the tax percentage below and above Rs. 2000 be x% and y% respectively.

Let the value of the goods purchased be M.

Let the amount of tax paid on M be T.

Let the amount of tax paid on Rs. 2000 be P.

Let the amount of tax paid on Rs. 10000 (i.e., Rs. 8000 above Rs. 2000) be Q.

Then, we have

Mx/100 + (M - 2000)y/100 = T ----- (1)

2000x/100 + P = T ----- (2)

8000y/100 + Q = T ----- (3)

Subtracting (2) from (1), we get

(M - 2000)y/100 - 2000x/100 = 0

(M - 2000)y = 2000x ----- (4)

Subtracting (2) from (3), we get

8000y/100 - 2000x/100 = 360

40y - 10x = 18 ----- (5)

Multiplying (4) by 10, we get

(M - 2000)10y = 20000x

Dividing by 2000 and substituting in (5), we get

40y - (M - 2000)y/100 = 18 ----- (6)

Substituting M = 6000 and T = 320 in (1), we get

6000x/100 + 4000y/100 = 320

60x + 40y = 32 ----- (7)

Substituting M = 12000 and T = 680 in (1), we get

12000x/100 + 10000y/100 = 680

120x + 100y = 68 ----- (8)

Multiplying (7) by 5, we get

300x + 200y = 160 ----- (9)

Subtracting (9) from (8), we get

-180x - 300y = -92

Multiplying by -1/3, we get

60x + 100y = 92/3 ----- (10)

Adding (6) and (10), we get

140y = 154/3

y = 11/3

Substituting in (10), we get

60x + 100(11/3) = 92/3

60x = 2/3

x = 1/30

Therefore, (X - Y) = (1/30 - 11/300) = 1/150.

Hence, the value of (X - Y) is 1/150.

Answered by Wizius Careers · View profile

Community Answer

A shopkeeper charges sales tax of X% up to Rs 2000 and above it he cha...

SOLUTION :--
Tax on Rs 2000 = X%
Tax on Above 2000 = Y% (GIVEN)
ATQ:
2000 × X% + (remaining) 4000 × Y% = 320 [1st Case]
2000 × X/100 + 4000 × Y/100 = 320
20x + 40y = 320 [Equation 1]
Again,
2000 × X% + (remaining) 10000 × Y % = 680 [2nd Case]
2000 × X/100 + 10000 × Y/100 = 680
20x + 100y = 680 [Equation 2]
Now,
Subtracting Equation 2 from 1...
20x + 40y = 320
20x + 100y = 680
-60y = -360
Y = 6
Now, putting the value of (Y = 6) in Equation 1 we, get...
20x + 40y = 320
20x + 40×6 = 320
20x = 320-240
X = 80/20
X = 4
Now we have the value of both X and Y where (X = 4) & (Y = 6), so we can easily find (X - Y) = ( 4 - 6) i.e = -2
Hence, (X - Y) = -2 (ans)...

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A shopkeeper charges sales tax of X% up to Rs 2000 and above it he charges Y%. A customer pays total tax of Rs 320, when he purchased the goods worth Rs 6000 and he also pay's the total tax of rupees Rs 680 for the goods worth Rs 12000. Find the value of (X - Y).? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper charges sales tax of X% up to Rs 2000 and above it he charges Y%. A customer pays total tax of Rs 320, when he purchased the goods worth Rs 6000 and he also pay's the total tax of rupees Rs 680 for the goods worth Rs 12000. Find the value of (X - Y).? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper charges sales tax of X% up to Rs 2000 and above it he charges Y%. A customer pays total tax of Rs 320, when he purchased the goods worth Rs 6000 and he also pay's the total tax of rupees Rs 680 for the goods worth Rs 12000. Find the value of (X - Y).?.

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