hamburger menu
All Coursesall course arrow
adda247
reward-icon
adda247
    arrow
    arrow
    arrow
    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 i
    Question

    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%.

    A.

    6.4%

    B.

    8.2%

    C.

    9.1%

    D.

    8.6%

    Correct option is A

    Given:

    Decrease in length and breadth = 10% and 20%

    Increase in height = 30%

    Formula Used:

    Volume of cuboid =L×B×H 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 = 0.064lbhlbh×100=6.4%\frac{0.064lbh}{lbh} \times 100 = 6.4\% ​decrease

    Alternative Method:

    Successive Percentage = x+y+xy100x + y +\frac{xy}{100}​​

    =1020+(10)(20)100 = -10-20 + \frac{(-10)(-20)}{100}​​

    = -30 + 2 = -28%

    Now successive formula with -28% and +30%

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

    = 2 - 8.4

    = -6.4%

    Negative sign means decrease in percentage

    Free Tests

    Free
    Must Attempt

    SSC GD PYP (Held on 4 Feb 2025 S1)

    languageIcon English
    • pdpQsnIcon80 Questions
    • pdpsheetsIcon160 Marks
    • timerIcon60 Mins
    languageIcon English
    Free
    Must Attempt

    SSC GD Constable Exam Day Based Mock 1

    languageIcon English
    • pdpQsnIcon80 Questions
    • pdpsheetsIcon160 Marks
    • timerIcon60 Mins
    languageIcon English
    Free
    Must Attempt

    Mathematics Section Test 1

    languageIcon English
    • pdpQsnIcon20 Questions
    • pdpsheetsIcon40 Marks
    • timerIcon25 Mins
    languageIcon English

    Similar Questions

    test-prime-package

    Access ‘Delhi Police Constable’ Mock Tests with

    • 60000+ Mocks and Previous Year Papers
    • Unlimited Re-Attempts
    • Personalised Report Card
    • 500% Refund on Final Selection
    • Largest Community
    students-icon
    446k+ students have already unlocked exclusive benefits with Test Prime!

    Similar Questions

    Our Plans
    Monthsup-arrow