Question

Namrata purchased 1375 kg of rice. she sold one fourth of the total quantity at a loss of 10%,half at a profit of 8%.at what %profit should she cell the remaining rice to make 30% profit in the whole transaction?

Answer 1

Total qty of rice purchased = 1375 kg
Let Cost Price of rice for Namrata = p per kg
So, cost price of 1375 kg rice = 1375p

She sold 1/4 of total at 10% loss, so
1/4 x 1375 = 343.75 kg

Cost price of 343.75 kg rice = 343.75p

She sold it at 10% loss, 
So SP of 343.75 kg of rice will be

90% of CP = 90% of 343.75p = 309.375p
Similarly, she sold 1/2 of total at profit of 8%
1/2 x 1375 = 687.5 kg
Cost price of 687.5 kg of rice = 687.5p

She sold it at 8% profit, 
So SP of 687.5 kg of rice will be
108% of CP = 108% of 687.5p = 742.5p
Now,
Let SP of remaining qty of rice be Z, so we have
In order to gain 30% profit in whole transaction, she needs total selling price to be 130% of total cost price.
total CP = 1375p
total SP = 130% of 1375p = 1787.5p
So,
1787.5p = 309.375p + 742.5p + Z

1787.5p = 1051.875p + Z

Z = 735.625p
SP of remaining qty = 735.625p
Remaining qty = 1375 [ 1 - 1/2 -1/4 ] = 1375 [ 1/4 ]
1/4 x 1375 = 343.75 kg

Cost price of 343.75 kg rice = 343.75p
Now, SP is 735.625p
Profit = (SP - CP)/CP x 100
Profit = (735.625p - 343.75p)/343.75p x 100

Profit = 391.875p / 343.75p x 100
Profit = 114%
Therefore, at 114% profit should she cell the remaining rice to make 30% profit in the whole transaction

Answer 2

Solve Mixture & Alligation method