A shopkeeper bought a sofa-set, a centre table and a dining table for ₹15,000, ₹3,000 and ₹7,000, respectively. He sold the sofa-set at 20% profit and the centre table at 15% profit. At what profit percentage should he sell the dining table to earn 18% on the whole transaction?

Let the cost prices of the sofa-set, centre table, and dining table be CP
1
​
,CP
2
​
, and CP
3
​
respectively.

CP
1
​
=15000
CP
2
​
=3000
CP
3
​
=7000
The ratio of their cost prices is:

CP
1
​
:CP
2
​
:CP
3
​
=15000:3000:7000=15:3:7
Total parts =15+3+7=25

Let the required profit percentage on the dining table be x%.
Using the weighted average formula for overall profit percentage:

25
15×20%+3×15%+7×x%
​
=18%
300+45+7x=18×25
345+7x=450
7x=450−345
7x=105
x=15%
Thus, he should sell the dining table at a profit of 15%.