Question

A firm has tractors of four models A, B, C and D. Four tractors (two of model B and one each of models C and D) plough a field in 2 days. Two model A tractors and one model C tractor take 3 days to do this job. Three tractors one each of models A, B and C take 4 days to do the same task. How long will it take to do the job if a team is made up of four tractors of different models?

• A. 10/7 days
• B. 14/7 days
• C. 13/7 days
• D. 12/7 days

Answer 1

The correct option is D

12/7 days

Method 1:
$\frac{2}{B}+\frac{1}{C}+\frac{1}{D}=\frac{1}{2}.............\left(i\right)$

$\frac{2}{A}+\frac{1}{C}=\frac{1}{3}...................\left(ii\right)$

And $\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{4}..........\left(iii\right)$

On subtracting (i) and (ii) we get,

$\frac{2}{A}-\frac{2}{B}-\frac{1}{D}=\frac{1}{6}...................\left(iv\right)$

On subtracting (iii) from (ii) we get

$\frac{1}{A}-\frac{1}{B}=\frac{1}{12}$

Therefore ,$\frac{1}{B}=\frac{1}{A}-\frac{1}{12}.................\left(v\right)$

From (ii), $\frac{1}{C}=\frac{1}{3}-\frac{2}{A}.......................\left(vi\right)$

Using (i), (v) and (vi), we get

$\frac{1}{D}=\frac{1}{2}-2(\frac{1}{A}-\frac{1}{12})-(\frac{1}{3}-\frac{2}{A})=\frac{1}{3}$

Therefore, $\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+\frac{1}{D}=\frac{1}{4}+\frac{1}{3}=\frac{7}{12}$

Hence time taken to complete the job $=\frac{12}{7}$ days.

Method 2: Using percentage approach (Recommanded)
Given that
2B+C+D=50 ............(1)
2A+C=33.33.............(2)
A+B+C=25...............(3)

$\left(3\right)\times 2-\left(2\right)$
2B+C=16.66
Substituting in (1)
D=33.33$\%$
From (3) and adding D to it we get
A+B+C+D=68.88$\%$=$\frac{12}{7}$ days.