Nitesh does a certain work such that everydays his efficiency falls by 19% of that on the previous day. If he manages to finish the whole work in 10 days, then find the number of days in which he can completeanother work which is 90% more than thiswork and where his efficiency everydays fallsby10% of that on the previous
Answers
Answer:
Work will be completed in 20 days
Step-by-step explanation:
Nitesh does a certain work such that everydays his efficiency falls by 19% of that on the previous day.
Work on 1st Day = A
work on next day = A - (19/100)A = 0.81A
Work on next of next day = 0.81A - (19/100)0.81A = 0.81²A
This is a GP
where first term = A r = common ration = 0.81
Work done in 10 days
= A ( 1 - 0.81¹⁰)/(1 - 0.81)
= A ( 1 - 0.81¹⁰)/(0.19)
90% more Work = 1.9 * (A ( 1 - 0.81¹⁰)/(0.19)
= 10A ( 1 - 0.81¹⁰)
efficiency everydays falls by 10%
work on next day = A - (10/100)A = 0.9A
Let say work is completed on n days
Work in n days
= A (1 - 0.9ⁿ)/(1 - 0.9)
= A(1 - 0.9ⁿ)/(0.1)
= 10A(1 - 0.9ⁿ)
10A ( 1 - 0.81¹⁰) = 10A(1 - 0.9ⁿ)
=> 1 - 0.81¹⁰ = 1 - 0.9ⁿ
=> 0.81¹⁰ = 0.9ⁿ
=> 0.9²⁰ = 0.9ⁿ
=> n = 20
Work will be completed in 20 days