1 Marks Question

Question 11 Mark

Fill in the blanks. A tap can fill a tank in $6$ hours. The part of the tank filled in $1 $ hour is _______.

Answer

A tap can fill a tank in $6$ hours.
The part of the tank filled in $1$ hour is $\frac{1}{6}.$
Solution:
A tap can fill a tank in $6$ hours. In $1$ hour,
$\frac{1}{6}$ of the tank is filled.

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MCQ 21 Mark

Tick the correct answer in the following: A alone can finish a piece of work in $10 $ days which $B$ alone can do in $15$ days. If they work together and finish it, then out of total wages of $Rs. 3000,$ A will get:

A
$Rs. 1200$
B
$Rs. 1500$
✓
$Rs. 1800$
D
$Rs. 2000$

Answer

Correct option: C.

$Rs. 1800$

Total wages $= Rs. 3000$
$A's\ 1$ days work $=\frac{1}{10}$
$B's\ 1$ days work $=\frac{1}{15}$
$\therefore$ Ratio in their work $=\frac{1}{10}:\frac{1}{15}$
$=\frac{3:2}{30}=3:2$
$\therefore A's$ share $= Rs. 3000\times\frac{3}{3+2}$
$=\text{Rs}.\frac{3000\times3}{5}=\text{Rs}.1800$

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Question 31 Mark

Fill in the blanks.
$A$ and $B$ working together can finish a piece of work in $6$ hours while $A$ alone can do it in $9$ hours. $B$ alone can do it in ______ hours.

Answer

$A$ and $B$ working together can finish a piece of work in $6$ hours while $A$ alone can do it in $9$ hours.
$B$ alone can do it in $18$ hours.
Solution:
$(A + B)'s\ 1$ hour work $=\frac{1}{6}$
$A's\ 1$ hour work $=\frac{1}{9}$
$B's\ 1$ hour work $=\frac{1}{6}-\frac{1}{9}=\frac{3-2}{18}=\frac{1}{18}$
Thus, $B$ takes $18$ hours to finish the work.

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Question 41 Mark

Fill in the blanks. If $A's$ one day's work is $\frac{3}{20},$ then A can finish the whole work in ______ days.

Answer

If $A's$ one day's work is $\frac{3}{20},$ then $A$ can finish the whole work in $\frac{20}{3}=6\frac{2}{3}$ days.
Solution: The time for completion is the reciprocal of the work done in one day. Therefore, $A$ can complete the whole work in $\frac{20}{3}=6\frac{2}{3}$ days.

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Question 51 Mark

Fill in the blanks.
A can do a work in $16$ hours and $B$ alone can do it in $24$ hours. If $A, B$ and $C$ working together can finish it in $8$ hours, then $C$ alone can finish it in ______ hours.

Answer

A can do a work in $16$ hours and $B$ alone can do it in $24$ hours. If $A, B$ and $C$ working together can finish it in $8$ hours, then $C$ alone can finish it in $48$ hours.
Solution:
$A's\ 1$ hour work $=\frac{1}{16}$
$B's\ 1$ hour work $=\frac{1}{24}$
$C's\ 1$ hour work $=\frac{1}{\text{x}}$
$(A + B + C)'s\ 1$ hour work $=\frac{1}{8}$
Therefore, $\frac{1}{\text{x}}=\frac{1}{8}-\frac{1}{16}-\frac{1}{24}=-\frac{6-3-2}{48}=\frac{1}{48}$
or, $X = 48$ hours.
Thus, $C$ alone takes $48$ hours to complete the work.

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