Select the correct answer from the options provided.

The ratio of the duration required for a senior technician, an associate technician, and an apprentice technician to finish a maintenance service individually is 1 : 2 : 3 respectively. If 10 senior, 15 associate, and 18 apprentice technicians work together to complete a service and the total service charge they received is Rs. 1410, then what is the total service charge for 10 senior, 12 associate, and 15 apprentice technicians?

The correct option is 1260 Rs.

Step-by-step Explanation:

1. Determine Efficiency Ratio:
The ratio of the duration required by a Senior (S), Associate (A), and Apprentice (P) technician to complete a task individually is:

$\text{Time Ratio}=1:2:3$

Since work rate (efficiency) is inversely proportional to time:

$\text{Efficiency Ratio}=\frac{1}{1}:\frac{1}{2}:\frac{1}{3}$

Multiplying by the LCM (6) to clear fractions gives:

$\text{Efficiency Ratio (S : A : P)}=6:3:2$

2. Calculate Value per Efficiency Unit from First Group:
For 10 senior, 15 associate, and 18 apprentice technicians, total efficiency units are:

$\text{Total Units}=(10\times 6)+(15\times 3)+(18\times 2)$

$\text{Total Units}=60+45+36=141\text{units}$

Given total service charge = Rs. 1410:

$\text{Value of 1 unit}=\frac{1410}{141}=\text{Rs.}10$

3. Calculate Total Service Charge for Second Group:
For 10 senior, 12 associate, and 15 apprentice technicians, total efficiency units are:

$\text{Total Units}=(10\times 6)+(12\times 3)+(15\times 2)$

$\text{Total Units}=60+36+30=126\text{units}$

Therefore, total service charge:

$\text{Total Service Charge}=126\times 10=\text{Rs.}1260$