Question

A company processes a number of cheques every month. There are two type of cheques. Type 1 has an average amount of $75 and constitutes 61.90% of the total number of cheques. The other type, Type 2, has an average amount of $96. Type 1 cheques take 3 days on average to clear, while Type 2 cheques take 4 days on average to clear. If the total daily (collection) float for the two cheques is $6,903, how many cheques is the company processing every month? (Assume 30 days in a month.)

Answer 1

Given

Total daily ( Collection ) float for the two cheques is $ 6903

We know that Average daily float = weight of Type 1 cheques( Total no.of Cheques received in a day) ( Amount of Type 1 cheque )( No.of days to clear Type 1 Cheque) + weight of Type 2 cheque( Total no.of Cheques received in a day) ( Amount of Type 2 cheque )( No.of days to clear Type 2 Cheque)

Given Weight of Typle 1 cheque = 0.6190 or 61.90%

weight of Type 2 Cheque = 1- weigt of type 1 cheque

= 1-0.6190

= 0.381 or 38.10%

Hence Proportion of type 2 Cheques is 0.381 or 38.1%

No.of days needed to clear Type 1 Cheque = 3 days

No.of days needed to clear Type 2 Cheque = 4 days

Computation of No.of Cheques proceesed in a day:

Let the No.of Cheques received in a day be X

Average daily float = weight of Type 1 cheques( Total no.of Cheques received in a day) ( Amount of Type 1 cheque )( No.of days to clear Type 1 Cheque) + weight of Type 2 cheque( Total no.of Cheques received in a day) ( Amount of Type 2 cheque )( No.of days to clear Type 2 Cheque)

$ 6903= 0.6190( X ) ( $ 75) ( 3) + 0.381( X) ( $ 96)( 4)

$ 6903 = $ 139.2750 X + $ 146.3040

$ 6903= $ 285.579 X

$ 6903/ $ 285.579 = X

X = 24.17195

Hence No.of Cheques processed daily is 24.17195

Computation of No.of Cheques proceesed in a month

No.of Cheques that will be Processed in One month = No.of cheques processed in one day *30

= 24.17195*30

= 725.16

Hence 725.16 Cheques are Processed every month.