Question:
The number of days required by three persons A, B, C independently to complete a given work is as per the ratio \(3:4:6\). How many days are required for B and C together to complete the work?
Statements:
(I) A is \(100\%\) more efficient than C.
(II) C requires 27 days more than A to complete the work.
The number of days required by three persons A, B, C independently to complete a given work is as per the ratio \(3:4:6\). How many days are required for B and C together to complete the work?
Statements:
(I) A is \(100\%\) more efficient than C.
(II) C requires 27 days more than A to complete the work.
Show Hint
In time and work problems, ratios only give relative values. To find exact time, always determine the multiplying factor.
Updated On: Jul 15, 2026
- Statement (I) alone is sufficient to answer the question, but (II) alone is not sufficient.
- Statement (II) alone is sufficient to answer the question, but (I) alone is not sufficient.
- Both the statements (I) and (II) are sufficient to answer the question, but neither statement alone is sufficient.
- Both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Time taken to complete work is inversely proportional to efficiency.
If the ratio of days taken by A, B, and C is:
\[
3:4:6
\]
then let their times be:
\[
3x,\;4x,\;6x
\]
To find the exact number of days for B and C together, we first need the value of \(x\).
Step 1: Checking Statement (I).
Given: A is \(100\%\) more efficient than C. This means: \[ E_A=2E_C \] Since time is inversely proportional to efficiency: \[ T_A=\frac{T_C}{2} \] This only confirms: \[ 3x=\frac{6x}{2} \] which is already consistent with the given ratio. No actual value of \(x\) is obtained. So, Statement (I) alone is not sufficient.
Step 2: Checking Statement (II).
Given: C requires 27 days more than A. From ratio: \[ T_C-T_A=27 \] \[ 6x-3x=27 \] \[ 3x=27 \] \[ x=9 \] Thus, \[ T_B=4x=36 \] \[ T_C=6x=54 \] Now combined work rate: \[ \frac{1}{36}+\frac{1}{54} \] Taking LCM \(108\): \[ =\frac{3+2}{108} \] \[ =\frac{5}{108} \] So total time: \[ =\frac{108}{5} \] \[ =21.6 \text{ days} \] Thus, Statement (II) alone is sufficient. Hence, the correct answer is (B).
Step 1: Checking Statement (I).
Given: A is \(100\%\) more efficient than C. This means: \[ E_A=2E_C \] Since time is inversely proportional to efficiency: \[ T_A=\frac{T_C}{2} \] This only confirms: \[ 3x=\frac{6x}{2} \] which is already consistent with the given ratio. No actual value of \(x\) is obtained. So, Statement (I) alone is not sufficient.
Step 2: Checking Statement (II).
Given: C requires 27 days more than A. From ratio: \[ T_C-T_A=27 \] \[ 6x-3x=27 \] \[ 3x=27 \] \[ x=9 \] Thus, \[ T_B=4x=36 \] \[ T_C=6x=54 \] Now combined work rate: \[ \frac{1}{36}+\frac{1}{54} \] Taking LCM \(108\): \[ =\frac{3+2}{108} \] \[ =\frac{5}{108} \] So total time: \[ =\frac{108}{5} \] \[ =21.6 \text{ days} \] Thus, Statement (II) alone is sufficient. Hence, the correct answer is (B).
Was this answer helpful?
0
0
Top TG ICET Analytical Ability Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions
Top TG ICET Data Sufficiency Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions
Top TG ICET Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions