a) A motor vehicle has a book value of Sh 76,800. This motor vehicle was purchased before and depreciation…

Question

a) A motor vehicle has a book value of Sh 76,800. This motor vehicle was purchased before and depreciation was charged at 20% on reducing balance method. Find the original cost of the motor vehicle.

ScanSolve AI Tutor · Accepted Answer

Huu hapa ni ufumbuzi wa swali la 3(a):

a) Gari lina thamani ya kitabu (book value) ya Sh 76,800. Gari hili lilinunuliwa hapo awali na kushuka kwa thamani kulitozwa kwa 20% kwa kutumia njia ya salio pungufu (reducing balance method). Tafuta gharama halisi ya gari.

Andika formula ya kushuka kwa thamani kwa kutumia njia ya salio pungufu.
Formula ya kushuka kwa thamani kwa njia ya salio pungufu ni:
$V = P(1 - r)^n$
Ambapo:
- $V$ ni thamani ya kitabu (book value) baada ya kushuka kwa thamani.
- $P$ ni gharama halisi (original cost).
- $r$ ni kiwango cha kushuka kwa thamani (depreciation rate).
- $n$ ni idadi ya miaka.
Tambua taarifa zilizotolewa na uweke dhana.
- Thamani ya kitabu ( $V$ ) = Sh 76,800.
- Kiwango cha kushuka kwa thamani ( $r$ ) = 20% = 0.20.
- Kwa kuwa idadi ya miaka ( $n$ ) haijatajwa wazi, tunadhania kuwa kushuka kwa thamani kulitozwa kwa mwaka mmoja ( $n=1$ ).
Badilisha maadili kwenye formula na utatue kwa $P$ .
$76,800 = P(1 - 0.20)^1$ $76,800 = P(0.80)$
Kokotoa $P$ .
Ili kupata $P$ , gawanya pande zote mbili kwa 0.80:
$P = \frac{76,800}{0.80}$ $P = 96,000$
Gharama halisi ya gari ni:
$\text{Sh } 96,000$

A) A motor vehicle has a book value of Sh 76,800. This motor vehicle was purchased before and depreciation was charged at 20% on reducing balance method. Find the original cost of the motor vehicle.

Answer

Step-by-step solution

Andika formula ya kushuka kwa thamani kwa kutumia njia ya salio pungufu.

Tambua taarifa zilizotolewa na uweke dhana.

Badilisha maadili kwenye formula na utatue kwa $P$ .

Kokotoa $P$ .

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