He must mix 15 kg of sugar at 50 p per kg.

Step-by-step solution (Quick Scoop)

Let the required amount of 50 p sugar be x kg.

  • Sugar A: 50 p per kg, quantity = x kg
  • Sugar B: 34 p per kg, quantity = 25 kg
  • Selling price of mixture = 44 p per kg
  • Profit = 10% on total cost

1. Total cost (outlay)

Cost of sugar at 50 p:

CostA=50x pence\text{Cost}_A=50x\text{ pence}CostA​=50x pence

Cost of sugar at 34 p:

CostB=34×25=850 pence\text{Cost}_B=34\times 25=850\text{ pence}CostB​=34×25=850 pence

Total cost:

Total cost=50x+850 pence\text{Total cost}=50x+850\text{ pence}Total cost=50x+850 pence

2. Total selling price with 10% profit

10% gain means:

Selling price=1.10×Total cost\text{Selling price}=1.10\times \text{Total cost}Selling price=1.10×Total cost

Total quantity of mixture:

Total kg=x+25\text{Total kg}=x+25Total kg=x+25

Given selling price per kg = 44 p, so:

Total selling price=44(x+25) pence\text{Total selling price}=44(x+25)\text{ pence}Total selling price=44(x+25) pence

Thus:

44(x+25)=1.10(50x+850)44(x+25)=1.10(50x+850)44(x+25)=1.10(50x+850)

3. Solve the equation

First, remove the decimal:

44(x+25)=1110(50x+850)44(x+25)=\frac{11}{10}(50x+850)44(x+25)=1011​(50x+850)

Multiply both sides by 10:

440(x+25)=11(50x+850)440(x+25)=11(50x+850)440(x+25)=11(50x+850)

Expand both sides:

440x+11000=550x+9350440x+11000=550x+9350440x+11000=550x+9350

Rearrange:

11000−9350=550x−440x11000-9350=550x-440x11000−9350=550x−440x

1650=110x1650=110x1650=110x

x=1650110=15x=\frac{1650}{110}=15x=1101650​=15

So, the man must mix 15 kg of sugar at 50 p per kg with 25 kg of sugar at 34 p per kg.

Final Answer

He should mix 15 kg of sugar at 50 p per kg.