Sunita stitches as fast as Tara and Usha put together. Sunita and Tara, working together, can stitch a batch of school uniforms in 6 days, while Usha alone needs 30 days for the batch. How many days would Tara alone need?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15 days
Work in one day is the rate. Sunita’s rate equals Tara’s rate plus Usha’s rate.
Let Tara and Usha do \(T\) and \(U\) of the batch in a day. Sunita does \(T+U\)
Sunita and Tara together: \(\displaystyle (T+U)+T=2T+U=\frac{1}{6}\)
Usha alone: \(\displaystyle U=\frac{1}{30}\)
\(\displaystyle 2T=\frac{1}{6}-\frac{1}{30}=\frac{5-1}{30}=\frac{4}{30}\), so \(\displaystyle T=\frac{2}{30}=\frac{1}{15}\)
Tara alone needs 15 days.
Why the other options are incorrect
Option (1) 10 days — Incorrect. Then \(2T+U=\frac{2}{10}+\frac{1}{30}=\frac{7}{30}\), which is more than \(\frac{1}{6}=\frac{5}{30}\).
Option (2) 12 days — Incorrect. Then \(2T+U=\frac{1}{6}+\frac{1}{30}\); the pair would finish in less than 6 days.
Option (4) 20 days — Incorrect. Then \(2T+U=\frac{1}{10}+\frac{1}{30}=\frac{4}{30}\), less than \(\frac{5}{30}\).