Find the total percentage change in the volume of a cuboid if its length and breadth are decreased by 10% and 20%, respectively, while its height is increased by 30%.

Correct option is A

Given:

Decrease in length and breadth = 10% and 20%

Increase in height = 30%

Formula Used:

Volume of cuboid =$$L \times B \times H$$​​

where L,B and H are length, breadth and height of cuboid respectively

Solution:

Let the length, breadth and height of cuboid initially be l,b and h respectively

Then volume = lbh

Then decreased length  = l - 20% of l = 0.9l

Decreased breadth = b - 20% of b = 0.8b

Increased height = h + 30% of h = 1.3h

New Volume = (0.9l)(0.8b)(1.3h) = 0.936lbh

Change in volumle = lbh - 0.936lbh = 0.064lbh

Percent change = $$\frac{0.064lbh}{lbh} \times 100 = 6.4\%$$​decrease

Alternative Method:

Successive Percentage = $$x + y +\frac{xy}{100}$$​​

​$$= -10-20 + \frac{(-10)(-20)}{100}$$​​

= -30 + 2 = -28%

Now successive formula with -28% and +30%

​$$= -28+30 + \frac{(-28)(30)}{100}$$​​

= 2 - 8.4

= -6.4%

Negative sign means decrease in percentage