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A person working in sales department draws Rs. y as basic salary. Further he gets 10% as commission for every penny more than 1 lakh brought in as sales. He also gets 20% as bonus for every penny more than 2 lakhs he brought in as sales. For a particular sales amount, he receives Rs. 50000 as total salary whereas he would have received only Rs. 15000 for half the sale amount. What is the value of y?

A person working in sales department draws Rs. y as basic salary. Further he gets 10% as commission for every penny more than 1 lakh brought in as sales. He also gets 20% as bonus for every penny more than 2 lakhs he brought in as sales. For a particular sales amount, he receives Rs. 50000 as total salary whereas he would have received only Rs. 15000 for half the sale amount. What is the value of y? Correct Answer 10000

Let the sales he made be Rs. x

If sales are less than 1 lakh, he would have received only basic pay which should be same for half the sales.

∴ Sales > 1 lakh

Let us assume 200000 > x > 100000

Half the sales will be less than 100000

∴ Salary received them = Basic pay = Rs. 15000

Salary received for sale of Rs. x = Basic pay + Commission of 10%

⇒ 50000 = 15000 + (x – 100000) × 10/100

⇒ x = 450000

It contradicts the assumption

Let us assume x > 200000

Salary received = Basic pay + Commission of 10% + Bonus of 20%

⇒ 50000 = y + (x – 100000) × 10/100 + (x – 200000) × 20/100

100000 = y + 0.3x      ---- 1

Maximum value of x = 100000/0.3 = Rs. 33333 1/3

∴ Half of sales is always less than Rs. 200000

∴ No bonus is paid when sales is halved

⇒ 15000 = y + 10/100 × (x/2 – 100000)

⇒ 25000 = y + 0.05x   ---- 2

Equation 1 – Equation 2

⇒ 75000 = 0.25x

⇒ x = 300000

Substituting in equation 1

⇒ y = Rs. 10000

∴ The value of y is Rs. 10000.

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