03 Percentage Profit and Loss
4. Successive Increment/Decrement
Alternatively we can use the successive change formula,
Effective percentage increase \( = \left( {x + y + \frac{{xy}}{{100}}} \right)\% \)
If a quantity changes by three consecutive changes of \(x\%\), \(y\%\) and \(z\%\), then the effective percentage change is: \[\left[ {x + y + z + \frac{{xy}}{{100}} + \frac{{yz}}{{100}} + \frac{{zx}}{{100}} + \frac{{xyz}}{{10000}}} \right]\]
For decrement we can use – sign in place of + sign. Suppose a number is decreased by \(x\%\) then by \(y\%\), if the initial value of the number is \(n\), then
Effective percentage change \( = \left( {(-x)+(-y) + \frac{{xy}}{{100}}} \right)\% \) \( = \left( {-x-y + \frac{{xy}}{{100}}} \right)\% \)
Questions 01: If a number is first increased by 30%, then by 50%. Find the net percentage change in the number.
Questions 02: If a number is first decreased by 30%, then by 40%. Find the net percentage change in the number.
Questions 03: Amit purchased a flat at Rs. 1 lakh and Binay purchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then:
(1) Amit paid Rs. 275 to Binay(2) Amit paid Rs. 475 to Binay
(3) Amit paid Rs. 2750 to Binay
(4) Amit paid Rs. 475 to Amite
We can use successive increment here.
Flat worth after 2
years = 1×1.1×1.1 lacs = Rs 121000.
Plot worth after 2 years = 1.1×1.05×1.05 lacs = Rs 121275.
Therefore Amit paid Rs. 275 to Binay as difference due to exchange.