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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
x $alpha$ $1 over z$
So, we can say that
x $alpha$ $y over z$
x = k $y over z$ …….(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 = k $900 over 10$
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 = k $660 over 12$
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

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

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?

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

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 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

cross times

16 = 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?

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

cross times

16 = 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.

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

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?

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

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

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

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

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?

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

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

480 over d

d = 24 days
Final Answer:
Hence, the number of days taken by 20 men to reap the field are 24 days.

Identify the common noun among the following

Explanation-A common noun is a name of a place , person , thing, idea or animal. It does not give any specifications. Hence opt a is the correct answer.

Identify the common noun among the following

Explanation-A common noun is a name of a place , person , thing, idea or animal. It does not give any specifications. Hence opt a is the correct answer.

Identify the definition of ‘oxymoron’.

Explanation-An oxymoron is a figure of speech that combines contradictory words with opposing meanings. Hence opt d is the correct answer.

Identify the definition of ‘oxymoron’.

Explanation-An oxymoron is a figure of speech that combines contradictory words with opposing meanings. Hence opt d is the correct answer.

parallel

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Explanation-Analogy means a correspondence or partial similarity. Hence opt b is the correct answer.

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Identify the definition of ‘supporting detail’.

Explanation-supporting details provide information to clarify or prove or to explain the main idea. Hence opt a is the correct answer.

Identify the definition of ‘supporting detail’.

Explanation-supporting details provide information to clarify or prove or to explain the main idea. Hence opt a is the correct answer.

Identify synonym for the word ‘perfect’.

Synonyms are usually the words that have same meaning to the other word. The word ideal also has same meaning as that of the word ‘perfect’. Hence opt d is the correct answer.

Identify synonym for the word ‘perfect’.

Synonyms are usually the words that have same meaning to the other word. The word ideal also has same meaning as that of the word ‘perfect’. Hence opt d is the correct answer.

parallel

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Reflexive pronouns are words like yourself, himself, herself, ourselves and refer to a person or thing. Hence opt c is the correct answer.

Identify the reflexive pronoun among the following.

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Identify past tense of the word ‘tread’

past tense means a tense expressing an action that has happened some time ago. Among the given options opt a is in the past tense form. Hence it is the correct answer.

Identify past tense of the word ‘tread’

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Rhyming words means usually the words that end with an identical sound to one another. Among given options seize is the word that rhymes with please. Hence opt-c is the correct answer.

Identify the word that rhymes with ‘please’

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parallel

Identify antonym for the word ‘learn’

Antonyms are usually the words that have same meaning to the other word. The word miss has exactly opposite meaning as that of the word ‘learn’. Hence opt b is the correct answer.

Identify antonym for the word ‘learn’

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Synonyms are usually the words that have same meaning to the other word. The word mend also has same meaning as that of the word ‘repair’. Hence opt a is the correct answer.

Identify the synonym for the word ‘Repair’.

Synonyms are usually the words that have same meaning to the other word. The word mend also has same meaning as that of the word ‘repair’. Hence opt a is the correct answer.

parallel

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