Question : Tina can do a work in 15 days and Manya can do the same work in 18 days. If they worked for 6 days, then what is the fraction of work is left?
Option 1: $\frac{4}{15}$
Option 2: $\frac{8}{15}$
Option 3: $\frac{11}{15}$
Option 4: $\frac{11}{30}$
Correct Answer: $\frac{4}{15}$
Solution :
One day work of Tina = $\frac{1}{15}$
One day work of Manya = $\frac{1}{18}$
One day work of Tina and Manya = $\frac{1}{15}+\frac{1}{18}$ = $\frac{6+5}{90}$ = $\frac{11}{90}$
Six day work of Tina and Manya = $\frac{11}{90}\times6$ = $\frac{11}{15}$
Remaining work = $(1-\frac{11}{15})$ = $\frac{4}{15}$
Hence, the correct answer is $\frac{4}{15}$.
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