Maths-
General
Easy

Question

If 18 binders can bind 900 books in 10 days, how many binders will be required to bind 660 books in 12 days?

Hint:

Hint:
In a proportional relationship, the variables are related by a constant ratio(k). For example, the equation which can relate the two variables can be written in the form:
y = (constant) cross times x or y = k cross times x.
So, for solving these types of questions we need to create a proportional relationship between the variables. These relationships can be direct, inverse etc.

The correct answer is: 12 days.


    Let the number of binders be represented as x, the number of books be represented as y and the number of days be represented as z. Now, more books will mean we will require more binders so x and y will have a directly proportional relationship i.e
    x alpha y
    Now if more days are given, fewer binders will be required which means x and z have an inversely proportional relationship i.e
    alpha 1 over z
    So, we can say that
    alpha y over z
    x = ky over z …….(1)
    Where k is a proportionality constant
    Step 1 of 2:
    It is given that 18 binders can bind 900 books in 10 days. So,  x = 18, y = 900 and z = 10. Putting the values in equation (1)
    18 = k900 over 10
    k = fraction numerator 18 space cross times space 10 over denominator 900 end fraction = 1 fifth
    Step 2 of 2:
    Now we are asked to find the number of binders that will be required to bind 660 books in 12 days. Let the number of binders be “b”. So, x = b, y = 660 and z = 12. Putting the values in equation (1)
    b = k660 over 12
    Now, put the value of k =
    d = 1 fifth cross times space 660 over 12
    d = 11 binders
    Final Answer:
    Hence, 11 binders will be required to bind 660 books in 12 days.

    Related Questions to study

    General
    Maths-

    A fort had enough food for 80 soldiers for 60 days. How long would the food last if 20 more soldiers join after 15 days?

    Let the number of days be represented as x and the number of soldiers be represented as y. The number of days will decrease if the number of soldiers are increased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
    y = k over x ……..(1)
    Step 1 of 2:
    After 15 days, the food is sufficient for 80 soldiers for (60 – 15) days = 45 days. So,  x = 45 and y = 80. Putting the values in equation (1)
    80 = k over 45
    k = 80 cross times 45  = 3600
    Step 2 of 2:
    Now we are asked to find the number of days the food will last if 20 more soldiers will join after 15 days. So, the total number of students becomes 100. Let the number of days be “d”. So, x = d and y = 100. Putting the values in equation (1)
    100 = k over d
    Now, put the value of k = 3600
    d = 3600 over 100
    d = 36 days
    Final Answer:
    Hence, the food will last for 36 days if 20 more soldiers join after 15 days.

    A fort had enough food for 80 soldiers for 60 days. How long would the food last if 20 more soldiers join after 15 days?

    Maths-General
    Let the number of days be represented as x and the number of soldiers be represented as y. The number of days will decrease if the number of soldiers are increased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
    y = k over x ……..(1)
    Step 1 of 2:
    After 15 days, the food is sufficient for 80 soldiers for (60 – 15) days = 45 days. So,  x = 45 and y = 80. Putting the values in equation (1)
    80 = k over 45
    k = 80 cross times 45  = 3600
    Step 2 of 2:
    Now we are asked to find the number of days the food will last if 20 more soldiers will join after 15 days. So, the total number of students becomes 100. Let the number of days be “d”. So, x = d and y = 100. Putting the values in equation (1)
    100 = k over d
    Now, put the value of k = 3600
    d = 3600 over 100
    d = 36 days
    Final Answer:
    Hence, the food will last for 36 days if 20 more soldiers join after 15 days.
    General
    Maths-

    A hostel has enough food for 125 students for 16 days. How long will the food last if 75 more students join them?

    Let the number of days be represented as x and the number of students be represented as y. The number of days will decrease if the number of students are increased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
    y = k over x ……..(1)
    Step 1 of 2:
    It is given that a hostel has enough food for 125 students for 16 days i.e. x = 16 and y = 125. Putting the values in equation (1)
    125 = k over 16
    k = 125 cross times16  = 2000
    Step 2 of 2:
    Now we are asked to find the number of days the food will last if 75 more students join. So, the total number of students becomes 200. Let the number of days be “d”. So, x = d and y = 200. Putting the values in equation (1)
    200 = k over d
    Now, put the value of k = 2000
    d = 2000 over 200
    d = 10 days
    Final Answer:
    Hence, the food will last for 10 days if 75 more students join.

    A hostel has enough food for 125 students for 16 days. How long will the food last if 75 more students join them?

    Maths-General
    Let the number of days be represented as x and the number of students be represented as y. The number of days will decrease if the number of students are increased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
    y = k over x ……..(1)
    Step 1 of 2:
    It is given that a hostel has enough food for 125 students for 16 days i.e. x = 16 and y = 125. Putting the values in equation (1)
    125 = k over 16
    k = 125 cross times16  = 2000
    Step 2 of 2:
    Now we are asked to find the number of days the food will last if 75 more students join. So, the total number of students becomes 200. Let the number of days be “d”. So, x = d and y = 200. Putting the values in equation (1)
    200 = k over d
    Now, put the value of k = 2000
    d = 2000 over 200
    d = 10 days
    Final Answer:
    Hence, the food will last for 10 days if 75 more students join.
    General
    Maths-

    12 men can dig a pond in 8 days. How many men can dig it in 6 days?

    Let the number of days be represented as x and the number of men be represented as y. The number of men will increase if the number of days are decreased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
    y = k over x  ……..(1)
    Step 1 of 2:
    It is given that 12 men can dig a pond in 8 days i.e. x = 8 and y = 12. Putting the values in equation (1)
    12 = k over 8
    k = 12 cross times 8  = 96
    Step 2 of 2:
    Now we are asked to find the number of men if 6 days are taken by them. Let the number of men be “m”. So, x = 6 and y = m. Putting the values in equation (1)
    m = k over 6
    Now, put the value of k = 96
    m = 96 over 6
    m = 16 men
    Final Answer:
    Hence, 16 men can dig the pond in 6 days.

    12 men can dig a pond in 8 days. How many men can dig it in 6 days?

    Maths-General
    Let the number of days be represented as x and the number of men be represented as y. The number of men will increase if the number of days are decreased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
    y = k over x  ……..(1)
    Step 1 of 2:
    It is given that 12 men can dig a pond in 8 days i.e. x = 8 and y = 12. Putting the values in equation (1)
    12 = k over 8
    k = 12 cross times 8  = 96
    Step 2 of 2:
    Now we are asked to find the number of men if 6 days are taken by them. Let the number of men be “m”. So, x = 6 and y = m. Putting the values in equation (1)
    m = k over 6
    Now, put the value of k = 96
    m = 96 over 6
    m = 16 men
    Final Answer:
    Hence, 16 men can dig the pond in 6 days.
    parallel
    General
    Maths-

    If 32 men can reap a field in 15 days, in how many days can 20 men reap the same field?

    Let the number of days be represented as x and the number of men be represented as y. The number of men will increase if the number of days are decreased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
    y =  k over x ……..(1)
    Step 1 of 2:
    It is given that 32 men can reap a field in 15 days i.e. x = 15 and y = 32. Putting the values in equation (1)
    32 = k over 15
    k = 32 cross times 15  = 480
    Step 2 of 2:
    Now we are asked to find the number of days taken by 20 men. Let the number of days be “d”. So, x = d and y = 20. Putting the values in equation (1)
    20 = k over d
    Now, put the value of k = 480
    20 = 480 over d
    d = 480 over d
    d = 24 days
    Final Answer:
    Hence, the number of days taken by 20 men to reap the field are 24 days.

    If 32 men can reap a field in 15 days, in how many days can 20 men reap the same field?

    Maths-General
    Let the number of days be represented as x and the number of men be represented as y. The number of men will increase if the number of days are decreased so we can conclude that y is in inverse relationship with x. Let’s say the proportional relationship is given as
    y =  k over x ……..(1)
    Step 1 of 2:
    It is given that 32 men can reap a field in 15 days i.e. x = 15 and y = 32. Putting the values in equation (1)
    32 = k over 15
    k = 32 cross times 15  = 480
    Step 2 of 2:
    Now we are asked to find the number of days taken by 20 men. Let the number of days be “d”. So, x = d and y = 20. Putting the values in equation (1)
    20 = k over d
    Now, put the value of k = 480
    20 = 480 over d
    d = 480 over d
    d = 24 days
    Final Answer:
    Hence, the number of days taken by 20 men to reap the field are 24 days.
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