CAT Exam > CAT Questions > A shopkeeper charges sales tax of X% up to Rs...
Start Learning for Free
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).?
Most Upvoted Answer
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.
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.
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)...
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)...
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
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).?
Question Description
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 2024 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 2024 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).?.
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 2024 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 2024 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).?.
Solutions 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).? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of 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).? defined & explained in the simplest way possible. Besides giving the explanation of
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).?, a detailed solution 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).? has been provided alongside types of 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).? theory, EduRev gives you an
ample number of questions to practice 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).? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup