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Johny Deep, a salesman of a Mercedes Benz showroom offers a commission of x% on the first sale of worth Rs. 3000 and y% on the part of sale exceeding it. He gives Rs. 1100 as commission on a sale of Rs. 7000 and Rs. 1660 as commission on a sale of Rs. 11000. Find the value of x and y.  

Johny Deep, a salesman of a Mercedes Benz showroom offers a commission of x% on the first sale of worth Rs. 3000 and y% on the part of sale exceeding it. He gives Rs. 1100 as commission on a sale of Rs. 7000 and Rs. 1660 as commission on a sale of Rs. 11000. Find the value of x and y.   Correct Answer 18% and 14%

Given∶ 

A commission of x% on the first sale worth Rs. 3000.

And, y% on the part of sale exceeding it.

He gives Rs. 1100 as commission on a sale of Rs. 7000.

And Rs. 1660 as commission on a sale of Rs. 11000.

Formula Used∶

Basics of percentage.

Calculation∶

For a total sale of Rs. 7000,

⇒ (3000 × x) / 100 + (4000 × y) / 100 = 1100

⇒ 30x + 40y = 1100

⇒ 3x + 4y = 110       ....(1)

For a total sale of Rs. 11000

⇒ (3000 × x) / 100 + (8000 × y) / 100 = 1660

⇒ 30x + 80y = 1660

⇒ 3x + 8y = 166      ....(2)

Subtract eq.(1) from eq.(2), we get

⇒ 4y = 166 - 110

⇒ 4y = 56

⇒ y = 56/4 = 14%

Put y = 14% in eq.(1), we get

⇒ 3x + 4(14) = 110

⇒ 3x + 56 = 110

⇒ 3x = 110 - 56

⇒ 3x = 54

⇒ x = 54/3

⇒ x = 18%

∴ The value of x is 18% and y is 14%.

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