A salesman commission is 5% on all sales upto rs.10000and 4% on all sales exceeding this .he remits rs.31,100 to his parent company after deducting his commission .find the total sales
Answers
Let his total sales be x
His commission would be
= 5% of 10000 + 4% of (x-10000)
= 500 + 4x/100 - 400
= 100 + 4x/100
= 100 + x/25
The amount he pays to company
= x- (x/25 + 100)
= x - x/25 - 100
= 24x/25 - 100 = 31100
24x/25 = 31200
x = (31200 * 25) / 24 = 32500
total sales = 32500
- The total sales was equal to Rs. 32,500 .
Given :- A salesman commission is 5% on all sales upto Rs.10000and 4% on all sales exceeding this . He remits Rs.31,100 to his parent company after deducting his commission .
To Find :- The total sales ?
Solution :-
Let us assume that, total sales was Rs. x.
given that, 5% commission on sale up to Rs. 10,000.
So,
→ 5% of sale 10000 = (10000 * 5) / 100 = Rs.500 ---- Equation (1)
Now,
→ Left sale = Rs. (x - 10000)
→ commission on sale more than 10000 = 4% of (x - 10000) = 4 * (x - 10000)/100 = (1/25)(x - 10000) ------ Equation (2)
So, adding Equation (1) and Equation (2) we get,
→ Total commission on sales = 500 + {(1/25)(x - 10000)}
then,
→ Remits = Total sales - Total commission
→ Remits = x - [500 + {(1/25)(x - 10000)}] ---- Equation (3)
Now, we have given that, total remits is Rs. 31,100. Therefore, putting Equation (3) equals to total remits :-
→ x - [500 + {(1/25)(x - 10000)}] = 31100
→
→ x - {(1/25)(x - 10000)} = 31100 + 500
→ (25x - x + 10000)/25 = 31600
→ 24x + 10000 = 31600 × 25
→ 24x = 31600 × 25 - 10000
→ 24x = 25(31600 - 400)
→ 24x = 25 × 31200
dividing both sides by 24,
→ x = 25 × 1300
→ x = Rs.32,500 (Ans.)
Hence Total sales is Rs. 32,500.
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