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Riddhi, Siddhi and Tithi can do a piece of work in 30, 45 and 90 days respectively. In how many days can Riddhi do the total work if he is assisted by Siddhi and Tithi on every third day?

Riddhi, Siddhi and Tithi can do a piece of work in 30, 45 and 90 days respectively. In how many days can Riddhi do the total work if he is assisted by Siddhi and Tithi on every third day? Correct Answer 23 days

In one day, work done by Riddhi = 1/30

Work done by Riddhi in 2 days = 1/30 × 2 = 1/15

Work done by Riddhi, Siddhi, Tithi on 3rd day = 1/30 + 1/45 + 1/90 = (3 + 2 + 1)/90 = 1/15

Therefore, work done in 3 days is = 1/15 + 1/15 = 2/15

2/15th of the work will be completed at the end of 3 days.

The remaining work = 1 - 2/15 = 13/15

2/15th of work is completed in 3 days.

multiplying by 7, we will get

14/15 of work is completed in 21 days

Now remaining 1/15 work is completed in next 2 days by Riddhi

Hence total days = 21 + 2 = 23 days

Alternate method:

Let total work = LCM (30, 45, 90) = 90

So Riddhi 1 day ‘s work = 90/30 = 3 units & Siddhi’s 1 day work = 90/45 = 2 units & that of Tidhi = 90 / 90 = 1 unit

Now 1st day, Riddhi does = 3 units, 2nd day Riddhi does = 3 units & 3rd day all do = 3 + 2 + 1 = 6 units &

Now 4th day, Riddhi does = 3 units, 5th day Riddhi does = 3 units & 6th day all do = 3 + 2 + 1 = 6 units & so on.

So, work in every 3 days = 12 units

Multiplying by 7, we will get

Work in 21 days = 84 units

Now remaining work = 90 - 84 = 6 units, which is completed in next 2 days by Riddhi

Hence total days = 21 + 2 = 23 days

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