Question

A number p is increased by 20%, then decrease by 10%. If the final value is 1 620, find

the original value of p.​

Answer 1

1500.

Explanation:

We can use algebra to do this.

20% = 0.20 and 10% = 0.10.

We form an equation:

p + 0.20p - 0.10(p + 0.20p) = 1620

p + 0.20p - 0.10p - 0.02p = 1620

1.20p - 0.12p = 1620

1.08p = 1620

p = 1620/1.08

= 1500.

Answer 2

Increase something by its 20% means to consider its 120%:

`p\mapsto p\cdot(120)/(100) = (120p)/(100)=(6p)/(5)`

Decrease something by its 10% means to consider its remaining 90%:

`(6p)/(5)\mapsto (6p)/(5)\cdot(90)/(100)=(540p)/(500)=(27p)/(25)`

So, we have the equation

`(27p)/(25)=1620 \iff 27p=40500 \iff p=1500`