Question
The dimensions of a rectangular box are in the ratio of $2: 3: 4$ and the difference between the cost of covering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per $m ^2$ is Rs. 1,248 . Find the dimensions of the box.
✓
Answer
Ratio in the dimensions of a box $=2: 3: 4$
Difference in total cost $=$ Rs. 1,248
Difference in rates $=$ Rs. $9.50-$ Rs. $8=$ Rs. 1.50
Let length $(l)=2 x$
Then breadth (b) $=3 x$
And, height $(h)=4 x$
$\therefore$ Surface area $=2( l \times b + b \times h + h \times l )$
$=2(2 x \times 3 x +3 x \times 4 x +4 x \times 2 x )$
$=2\left(6 x^2+12 x^2+8 x^2\right)=2 \times 26 x^2=52 x^2$
First rate of paper $=$ Rs. 9.50 per $m ^2$
And, second rate $=8.00$ per $m ^2$
$\therefore$ First cost $=$ Rs. $52 x^2 \times 9.50$
And, second cost $=$ Rs. $52 x^2 \times 8$
$\therefore 52 x^2 \times 9.50-52 x^2 \times 8=1248$
$\Rightarrow 52 x^2(9.50-8)=1248$
$\Rightarrow 52 x^2(1.50)=1248$
$\Rightarrow x^2=\frac{1248}{52 \times 1.50}=\frac{1248 \times 100}{52 \times 150}=16$
$\Rightarrow x=\sqrt{16}=4$
$\therefore \text { Length }=2 x=2 \times 4=8 m$
$\text { Breadth }=3 x=3 \times 4=12 m$
$\text { Height }=4 x=4 \times 4=16 m$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Construct a quadrilateral ABCD, given that AB = 8cm, BC = 8cm, CD = 10cm, AD = 10cm and $\angle\text{A}=45^\circ.$
→Draw a line l. Take a point A outside the line. Through point A draw a line parallel to line l.
Some toffees are bought at the rate of 11 for Rs. 10 and the same number at the rate of 9 for Rs. 10. If the whole lot is sold at one rupee per toffee, the find the gain or loss percent on the whole transaction.
Construct a rectangle PQRS by taking two convenient adjacent sides. Name the point of intersection of diagonals as T. Using divider and ruler, measure the following lengths.
i. lengths of opposite sides, seg QR and seg PS.
ii. lengths of seg PQ and seg SR.
iii. lengths of diagonals PR and QS.
iv. lengths of seg PT and seg TR, which are parts of the diagonal PR.
v. lengths of seg QT and seg TS, which are parts of the diagonal QS.
Observe the measures. Discuss about the measures obtained by your classmates.
i. lengths of opposite sides, seg QR and seg PS.
ii. lengths of seg PQ and seg SR.
iii. lengths of diagonals PR and QS.
iv. lengths of seg PT and seg TR, which are parts of the diagonal PR.
v. lengths of seg QT and seg TS, which are parts of the diagonal QS.
Observe the measures. Discuss about the measures obtained by your classmates.
In the following figure RISK and CLUE are parallelograms. Find the measure of x.
Solve the following equation and verify your answer:
$\frac{3\text{x}+5}{4\text{x}+2}=\frac{3\text{x}+4}{4\text{x}+7}$
→$\frac{3\text{x}+5}{4\text{x}+2}=\frac{3\text{x}+4}{4\text{x}+7}$
Some measures are given in the figure, find the area of ☐ABCD.
Number of workshops organized by a school in different areas during the last five years are as follows:
Draw a histogram representing the above data.
| Year | No. of workshops |
| 1995-1996 | 25 |
| 1996-1997 | 30 |
| 1997-1998 | 42 |
| 1998-1999 | 50 |
| 1999-2000 | 65 |
ABCD is a rhombus whose diagonals intersect at O. If AB = 10cm, diagonal BD = 16cm, find the length of diagonal AC.
A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price, he still makes a profit of 50%. Find the ratio of the CP to the MP.