Satyam and Shivam can do work in 10 days and 15 days respectively. Both start the work together, after 4 days Satyam left the work. Shivam has to complete the remaining work. In how many days, does the total work get completed?

Satyam and Shivam can do work in 10 days and 15 days respectively.

So the LCM of 10 and 15 is 30 which can be assumed as the total work.

The efficiency of Satyam =  $$\frac{30}{10}$$ = 3 units/day

The efficiency of Shivam = $$\frac{30}{15}$$ = 2 units/day

Both start the work together, after 4 days Satyam left the work. Shivam has to complete the remaining work.

Let's assume the number of days taken by Shivam to complete the remaining work is 'y'.

$$4\times(3+2)+y\times2 = 30$$

$$4\times5+2y = 30$$

20+2y = 30

2y = 30-20 = 10

y = 5

The total number of days taken to complete the work = (4+y) = 4+5

= 9