8th Class Mathematics Direct and Inverse Proportions Question Bank Direct and Inverse Proportions

  • question_answer Match the following.
    Column - I Column - II
    (P) If the cost of 93m of a certain kind of plastic sheet is Rs. 1395, then what would it cost (in Rs.) to buy 105 m of such plastic sheet? (1) 42
    (Q) 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days? (2) 18
    (R) 18 men can reap a field in 35 days. For reaping the same field in 15 days; how many men are required? (3) 88
    (S) Suneeta types 1080 words in one hour. What is her GWPM (gross words per minute)? (4) 1575

    A)

    P Q R S
    4 3 1 2
                   

    B)

    P Q R S
    2 1 4 3

    C)

    P Q R S
    3 2 1 4
                   

    D)

    P Q R S
    1 3 2 4

    Correct Answer: A

    Solution :

              (P) Let the cost be Rs. X
    Cost of sheet (in Rs.) 1395 x
    Length of sheet 93 105
    It is the case of direct variation. \[\frac{1395}{93}=\frac{x}{105}\Rightarrow x=\frac{1395\times 105}{93}=1575\] So, cost of plastic sheet is Rs. 1575. (Q) Let the number of cows be x.
    No. of cows 55 x
    No. of days 16 10
    It is the case of inverse variation. \[\Rightarrow 55\times 16=x\times 10\] \[\Rightarrow x=\frac{55\times 16}{10}=88\] So, 88 cows will graze the field in 10 days, (R) Let the number of men be x.
    No. of men 18 x
    No. of days 35 15
    It is the case of inverse variation. \[18\times 35=x\times 15\] \[\Rightarrow x=\frac{18\times 35}{15}=42\] So, 42 men can reap a field in 15 days. (S) Let the number of words \[=\text{ }x\]
    No. of words 1080 X
    Time (in minutes) 60 1
    It is the case of direct variation. \[\Rightarrow x=\frac{1080}{60}=18\] So, Sunita types 18 words per minute.

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