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Maths Solve The Following Question.1MARKS

Time and Work · Maharashtra Board STD 8 (MSBSHSE - English Medium). 5 questions.

Questions

Solve The Following Question.1MARKS

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5 questions · self-marked practice — reveal the answer and mark yourself.

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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Question 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:
  1. Rs. 1200
  2. Rs. 1500
  3. Rs. 1800
  4. Rs. 2000
Answer
  1. Rs. 1800
Solution:

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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