R and S can finish a work in 10 days, S and T can finish it in 12 days and T and R can finish in 8 days. In how many days will the work be finished if they all work simultaneously?

Question

Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 08 Jul, 2024 Shift 3)

Answer 1

Given:

R and S can finish a work in 10 days

S and T can finish a work in 12 days

T and R can finish a work in 8 days

Formula used:

Work done by R and S in 1 day = 1/10

Work done by S and T in 1 day = 1/12

Work done by T and R in 1 day = 1/8

Let work done by R, S, and T in 1 day be r, s, and t respectively

r + s = 1/10

s + t = 1/12

t + r = 1/8

Calculation:

Adding the three equations:

(r + s) + (s + t) + (t + r) = 1/10 + 1/12 + 1/8

⇒ 2r + 2s + 2t = 1/10 + 1/12 + 1/8

⇒ 2(r + s + t) = 1/10 + 1/12 + 1/8

⇒ r + s + t = 1/2 × (1/10 + 1/12 + 1/8)

Calculating the sum:

⇒ 1/10 + 1/12 + 1/8

⇒ 12/120 + 10/120 + 15/120

⇒ 37/120

So,

r + s + t = 1/2 × 37/120

⇒ r + s + t = 37/240

The work done by R, S, and T together in 1 day is 37/240

Therefore, the number of days required to finish the work is:

⇒ 240/37

∴ The correct answer is option 3 (240/37).

Download Solution PDF