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MATHS Assertion (A) & Reason (B) MCQ

Time and Work · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 8 questions.

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Assertion (A) & Reason (B) MCQ

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8 questions · timed · auto-graded

MCQ 11 Mark
Assertion (A): If 100 men together can do a work in 1 day then 1 man alone can do it in 100 days.
Reason (R): 100 men's 1 day's work $=1$.
Then, 1 man's 1 day's work $=\frac{1}{100}$.
  • A
    Both A and R are true and R is the correct explanation of A
  • B
    Both A and R are true but R is not the correct explanation of A
  • C
    A is true but R is false
  • D
    A is false but R is true
Answer
self
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MCQ 21 Mark
Assertion (A): If $A$ alone can do a work in 5 days and $B$ alone can do it in 10 days then the rates of working of $A$ and $B$ are in the ratio $5: 10$.
Reason (R): More the rate of working, lesser is the time taken to do the work.
  • A
    Both A and R are true and R is the correct explanation of A
  • B
    Both A and R are true but R is not the correct explanation of A
  • C
    A is true but R is false
  • D
    A is false but R is true
Answer
self
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MCQ 31 Mark
Assertion (A): $C$ does a work in 6 days, $B$ does the same work in 2 days and $A$ does it in 1 day.
Reason (R): $A$ is twice as fast as $B$ and $B$ is thrice as fast as $C$.
  • A
    Both A and R are true and R is the correct explanation of A
  • B
    Both A and R are true but R is not the correct explanation of A
  • C
    A is true but R is false
  • D
    A is false but R is true
Answer
self
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MCQ 41 Mark
Assertion (A): A alone can do a piece of work in 10 days. B is $50 \%$ more efficient than $A$. Then, $B$ can do that work alone in 5 days.
Reason (R): Ratio of rates of working of $A$ and $B=2: 3$.
  • A
    Both A and R are true and R is the correct explanation of A
  • B
    Both A and R are true but R is not the correct explanation of A
  • C
    A is true but R is false
  • D
    A is false but R is true
Answer
self
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MCQ 51 Mark
Assertion (A): A alone can do a piece of work in 10 days. $B$ is $50 \%$ more efficient than $A$. Then, $B$ can do that work alone in 5 days.
Reason (R): Ratio of rates of working of $A$ and $B=2: 3$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion $(A)$ is true but Reason $(R)$ is false.
  • ✓
    Assertion $(A)$ is false but Reason $(R)$ is true.
Answer
Correct option: D.
Assertion $(A)$ is false but Reason $(R)$ is true.
(D) Assertion $(A)$ is false but Reason $(R)$ is true.
Ratio of rates of working of $A$ and $B=100: 150=2: 3$.
Ratio of times taken by $A$ and $B$ to do a work $=\frac{1}{2}: \frac{1}{3}=3: 2$.
So, if $A$ does a work in 10 days then $B$ does it in $6 \frac{2}{3}$ days.
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MCQ 61 Mark
Assertion (A): $C$ does a work in 6 days, $B$ does the same work in 2 days and $A$ does it in 1 day.
Reason (R): $A$ is twice as fast as $B$ and $B$ is thrice as fast as $C$.
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion $(A)$ is true but Reason $(R)$ is false.
  • D
    Assertion $(A)$ is false but Reason $(R)$ is true.
Answer
Correct option: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
$\begin{array}{l}A: B=2: 1 \text { and } B: C=3: 1 \\ \Rightarrow A: B: C=6: 3: 1 .\end{array}$
Ratio of times taken by $A, B$ and $C$ to do a work $=\frac{1}{6}: \frac{1}{3}: 1=1: 2: 6$.
So, if $A$ takes 1 day to do a work, $B$ takes 2 days while $C$ takes 6 days to do it.
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MCQ 71 Mark
Assertion (A): If $A$ alone can do a work in 5 days and $B$ alone can do it in 10 days then the rates of working of $A$ and $B$ are in the ratio $5: 10$.
Reason (R): More the rate of working, lesser is the time taken to do the work.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion $(A)$ is true but Reason $(R)$ is false.
  • ✓
    Assertion $(A)$ is false but Reason $(R)$ is true.
Answer
Correct option: D.
Assertion $(A)$ is false but Reason $(R)$ is true.
(D) Assertion $(A)$ is false but Reason $(R)$ is true.
A's 1 day's work $=\frac{1}{5} ; B$ 's 1 day's work $=\frac{1}{10}$.
Rates of working of $A$ and $B=\frac{1}{5}: \frac{1}{10}=2: 1$.
So, $A$ is false.
Clearly, R is true as the rate of working and time taken are inversely proportional to each other.
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MCQ 81 Mark
Assertion (A): If 100 men together can do a work in 1 day then 1 man alone can do it in 100 days.
Reason (R): 100 men's 1 day's work $=1$.
Then, 1 man's 1 day's work $=\frac{1}{100}$.
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion $(A)$ is true but Reason $(R)$ is false.
  • D
    Assertion $(A)$ is false but Reason $(R)$ is true.
Answer
Correct option: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
A
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Assertion (A) & Reason (B) MCQ - MATHS STD 8 Questions - Vidyadip