Question

A wooden bookshelf has external dimensions as follows: Height =$110$ cm, Depth = $25$ cm, Breadth = $85$ cm. The thickness of the plank is $5$ cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is $20$ paise per ${cm}^2$ and the rate of painting is 10 paise per ${cm}^2$. Find the total expenses required for polishing and painting the surface of the bookshelf

• A. Rs $6275$
• B. Rs $4340$
• C. Rs $2525$
• D. Rs $1935$

Answer 1

The correct option is A Rs $6275$

External length (l) of bookshelf$=85㎝$

External breadth (b) of bookshelf$=25㎝$

External height (h) of bookshelf$=110㎝$

External surface area of book shelf while leaving out the front face of the shelf$=lh+2(lb+bh)$

$=(85\times 110)+2(85\times 25+25\times 110)$

$=9350+9750$

$=19100㎠$

Area if front face$=(85\times 110)-75\times 100+2(75\times 5)$

$=1850+760=2600㎠$

Area to be polished$=19100+2600=21700㎠$

Cost of polishing=Rs. $21700\times 0.20$=Rs.$4340$

Length, breadth and height of each row of bookshelf are

$75㎝,20㎝$ & $30㎝$ respectively. From the figure Area to be painted in $1$ row$=2(l+h)b+lh$

$=2(75+30)20+75\times 30$

$=6450㎠$

Area to be painted in $3$ rows$=3\times 6450=19350㎠$

Total cost of painting=Rs.$(19350\times 0.1)$=Rs. $1935$

Total expenses=Rs.$(4340+1935)$=Rs. $6275$