Question

Rakhi works in a store which offers the following forms of payment :

Get ₹5 on the first day, ₹10 on the second day, 15th on the third and so on. 
Get ₹540 per month. 

If she works for only 10 days,  which mode of payment she must choose? 

with steps and formula

Answer 1

She should choose the first method of Payment.

Answer 2

Answer:

First form of payment

Step-by-step explanation:

Find the amount she will get if she choose the first form of payment:

First Day = a1 =  ₹5

Common Differences = a2 - a1 = 10 - 5 =  ₹5

Find the amount she will get in nth day:

an = a1 + (n - 1)d

an = 5 + (n - 1)5

an = 5 + 5n - 5

an = 5n

Find the total amount she will get in n days:

Sn = n/2 (a1 + an)

Find the amount she will get in 10 days:

s10 = 10/2 (5 + 5(10))

s10 = 5(55)

s10 = ₹275

Find the amount she will get if she choose the second form of payment:

Assumed 30 days in a month

30 days = ₹540

1 day = 540 ÷ 30 = ₹18

10 days = 18 x 10 = ₹180

Conclusion:

Since ₹275 > ₹180

She should choose the first mode

Answer: First mode