Question

37. A can do a piece of work in 30 days while B alone can do it in 40 days. In how
many days can A and B working together do it? (1) 16 (1/7) (2) 17 (1/7) (3) 18 (1/7)
(4) 19 (117)​

Answer 1

work and work...xd

Step-by-step explanation:

assume they r doing same amount of work but difference is only efficiency

so let's assume they r doing 120 units of work

so A can do 120 units of work in 4 days (120/30)

and B cand do 120 units of work in 3 days.

so together they can do same work in 120/3+4

which is 17(1/7) that means option B

Answer 2

Answer :

• A and B together can complete the work within $\sf \: 17 \dfrac{1}{7} \: days$ . [Option 2]

Explanation :

We are given that A can do a piece of work within 30 days, while B can do the same work in 40 day's.

So,

Total work completed by A within a day = 1/30

Total work completed by B within a day = 1/40

★ Together work done by A and B within a day :

⇛ A + B

⇛ 1/30 + 1/40

⇛40 + 30 /1200

⇛ 70/1200

⇛ 7/20

★ Total no. of days required for A and B to finish the work together :

➟ $\sf \dfrac{1}{7/120}$

➟ $\sf \: 17 \dfrac{1}{7} \: days$

Therefore, A and B together can complete the work within $\sf \: 17 \dfrac{1}{7} \: days$ .

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★ Alternative Method :

We can calculate this by an alternative method too! [By LCM]

LCM of 30 & 40 is 120

• 120/30 = 4 [ A ]

• 120/40 = 3 [ B ]

Hence,

★ Total work done together :

⇛ 120/7

⇛ 17.15

⇛$\sf \: 17 \dfrac{1}{7} \: days$

Therefore, A and B together can complete the work within $\sf \: 17 \dfrac{1}{7} \: days$ .

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