QuestionRam, Shyam and Tarun can complete a work in 32 days, 60 days and 48 days respectively. All three started working together. After $x$ days, Ram left and Shyam left $x$ days before the work was completed. The work was completed at the end of $t$ days. If $x$ and $t$ are positive integers, the value of $t$ is

Studdy Solution
Solve for $t$.
First, find a common denominator for the fractions, which is 480. Rewrite the equation:
$\frac{15x}{480} + \frac{8(t-x)}{480} + \frac{10t}{480} = 1$
Simplify and combine terms:
$15x + 8t - 8x + 10t = 480$
$7x + 18t = 480$
Since $x$ and $t$ are integers, solve for $t$ by testing integer values for $x$ such that $7x + 18t = 480$.
Testing values, we find:
For $x = 24$:
$7(24) + 18t = 480$
$168 + 18t = 480$
$18t = 312$
$t = \frac{312}{18} = 17.33$
Since $t$ must be an integer, try $x = 30$:
$7(30) + 18t = 480$
$210 + 18t = 480$
$18t = 270$
$t = 15$
Thus, the value of $t$ is:
$$\boxed{15}$$