3 Marks Question

Question 13 Marks

Rakesh can do a piece of work in $20$ days. How much work can he do in $4$ days?

Answer

It is given that Rakesh can do a piece of work in $20$ days
$\therefore$ Rakesh' s $1$ day's work $=\frac{1}{20}$
$\therefore$ Rakesh's work for 4 days $=\frac{4}{20}=\frac{1}{5}$
Thus, he can do $\frac{1}{5}\text{th}$ of the work in 4 days.

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Question 23 Marks

Mohan takes $9$ hours to mow a large lawn. He and Sohan together can mow it in $4$ hours. How long will Sohan take to mow the lawn if he works alone?

Answer

Time taken by Mohan to do the work $= 9$ hours
Time taken by Mohan and Sohan to do the work $= 4$ hours
$\therefore$ Work done by Mohan $=\frac{1}{9}$
Work done by Mohan and Sohan $=\frac{1}{4}$
$\therefore$ Work done by Sohan $=\frac{1}{4}-\frac{1}{9}$
$=\frac{9-4}{36}=\frac{5}{36}$
Thus, Sohan can do the work in $\frac{36}{5}$ hours i. e. $7\frac{1}{5}$ hours.

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Question 33 Marks

If $9$ girls can prepare $135$ garlands in $3$ hours, how many girls are needed to prepare $270$ garlands in $1$ hour?

Answer

Number of garlands made by $9$ girls in $1$ hour$=\frac{135}{3}=45$
Number of garlands made by $1$ girl in $1$ hour
$\therefore$ Number of girls required to make $270$ garlands in $1$ hour $12$ days $=\frac{270}{5}=54$

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Question 43 Marks

A pipe can fill a cistern in $10$ hours. Due to a leak in the bottom it is filled in $12$ hours. When the cistern is full, in how much time will it be emptied by the leak?

Answer

When there is no leakage, the pipe can fill the cistern in $10$ hours
Thus, the pipe can fill $\frac{1}{10}\text{th}$ part of the cistern in $1$ hour
When there is leakage, the pipe can fill the cistern in $12$ hours Therefore, in case of leakage,
the pipe can fill $\frac{1}{12}\text{th}$ part of the cistern in $1$ hour.
Thus, in one hour, due to leakge, $\Big(\frac{1}{10}-\frac{1}{12}\Big)\text{th}$ or $\frac{1}{60}\text{th}$ part of the cistern is emptied
Hence, the cistern will be emptied by the leakage in 60 hours.

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Question 53 Marks

A cistern can be filled by one tap in $8$ hours, and by another in $4$ hours. How long will it take to fill the cistern if both taps are opened together?

Answer

Time taken by the first tap to fill the cistern $= 8$ hours
Time taken by the second tap to fill the cistern $= 4$ hours
$\therefore$ Work done by the first tap in $1$ hour $=\frac{1}{8}$
Work done by the second tap in $1$ hour $=\frac{1}{4}$
$\therefore$ Work done by both the taps in $1$ hour
$=\frac{1}{8}+\frac{1}{4}$ $=\frac{1+2}{8}=\frac{3}{8}$
Thus, both the taps together will fill the cistern in $\frac{8}{3}$ hours or $2\frac{2}{3}$ hours.

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Question 63 Marks

If $12$ boys earn Rs $840$ in $7$ days, what will $15$ boys earn in $6$ days?

Answer

Earnings of $12$ boys in $7$ days $=\text{ Rs. }840$
$\therefore$ Earnings of $12$ boys in $1$ day $=\text{Rs. }\frac{840}{7}=\text{Rs. }120$
$\therefore$ Earnings of $1$ boy in $1$ day $=\text{Rs.}\frac{120}{12}=\text{Rs. }10$
$\therefore$ Earnings of $1$ boy in $6$ days $=\text{Rs. }(10\times6)=\text{Rs. }60$
$\therefore$ Earnings of $15$ boys in $6$ days $=\text{Rs. }(60\times15)=\text{Rs. }900$

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Question 73 Marks

If $25$ men earn Rs $1000$ in $10$ days, how much will $15$ men earn in $15$ days?

Answer

Earnings of $25$ men in $10$ days $=\text{ Rs. }1000$
$\therefore$Earnings of 25 men in $1$ day $=\text{Rs. }\frac{1000}{10}=\text{Rs. }100$
$\therefore$ Earning of $1$ man in $1$ day $=\text{Rs.}\frac{100}{25}=\text{Rs. }4$
$\therefore$ Earnings of $1$ men in $15$ days $=\text{Rs. }(15\times4)=\text{Rs. }60$
$\therefore$ Earnings of $15$ men in $15$ days $=\text{Rs. }(60\times15)=\text{Rs. }900$

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Maths 3 Marks Question

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