If 9 engines consume 24 metric tons of coal when each is working 8 hours a day how much coal will be...........

Quant (SSC) Time and work

If 9 engines consume 24 metric tons of coal, when each is working 8 hours a day, how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?

23 metric tons

24 metric tons

25 metric tons

26 metric tons

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Explanation:

If M₁ persons can do W₁ work in H₁ hours and M₂ persons can do W₂ work in H₂ hours , M₁T₁W₂= M₂T₂W₁
Given:
? 4 engines latter type = 3 engines former type
∴ 8 engines latter type = 6 engines former type
M₁ = 9, H₁ = 8 hours/day, W₁ = 24 m tons
M₂ = 8, H₂ = 13 hours/day, W₂ = x m tons
Now, as M₁H₁W₂= M₂H₂W₁
⇒ 9 × 8 × x = 6 × 13 × 24
⇒ x = 6 × 13 × 24 / 9 x 8
⇒ x = 26 m tons