**Q) Sonal and Preeti started working on a project and they can complete the project in 30 days. Sonal worked for 16 days and Preeti completed the remaining work in 44 days. How many days would Preeti have taken to complete the entire project all by herself?**

**a) 20 days b) 55 days ****c) 46 days d) 60 days
**

**Ans:**

**Method 1:**

Let’s consider Sonal completes the work in S days and Preeti completes the work in P days

∴ Sonal’s 1 day’s work = 1/S

and Preeti’s 1 day’s work = 1/P

∴ (S + P)’s 1 day’s work = 1/S + 1/P = (S + P) / SP

Given that Sonal & Preeti together take 30 days

∴ (S + P)/SP = 1/30

∴ 30 (S + P) = SP ……….. (i)

Next, Sonal’s 16 days’ work = 16 x 1/S = 16/S

Balance work = 1 – 16/S = (S – 16)/S

This balance work is completed by Preeti

Since Preeti completes 1/P work in 1 day

Preeti will complete (S – 16)/S work in = [(S – 16)/S] /(1/P) = (S – 16)P/S days

(S – 16)P/S = 44 (given)

S P – 16 P = 44 S …………(ii)

By substituting value of AB in equation (ii), we get:

30 (S + P) – 16 P = 44 S

∴ 14 P = 14 S

∴ P = S

From equation (i), we get: 30 (2 P) = P x P

∴ P = 60 days

**Hence, Answer is [C]**

**Method 2:**

Let’s consider: Sonal’s 1 day’s work = S

and Preeti’s 1 day’s work = P

∴ S + P = 1/30 (given)

∴ 30 S + 30 P = 1 ….(i)

Given that Sonal for 16 days and Preeti worked for 44 days to complete the work

∴ 16 S + 44 P = 1 …. (ii)

From equation (i) & (ii), we get:

14 S – 14 P = 0

∴ S = P

From equation (i), we get:

30 S + 30 P = 1

∴ 60 P = 1

∴ P = 1/60

Since Time taken by Preeti to finish 1/60 work = 1 day

∴ Time taken by B to finish whole work = 1 /(1/60) = 60 days

**Hence, Answer is [C]**

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