The length of a rectangular blackboard is 8 m more than its breadth. If its length is increased by 7 m and its breadth is decreased by 4 m, its area remains unchanged. The length and breadth of the rectangular blackboard is :
(A) 24 m, 16 m
(B) 20 m, 24 m
(C) 28 m, 16 m
(D) 28 m, 20 m
Solution:
Let the breadth = x cm Then, length = (x + 8) m $$\eqalign{ & \therefore \left( {x + 8} \right)x = \left( {x + 15} \right)\left( {x - 4} \right) \cr & \Rightarrow {x^2} + 8x = {x^2} + 11x - 60 \cr & \Rightarrow x = 20 \cr} $$ So, length = 28 m and breadth = 20 m
12.
A typist uses a paper 30 cm by 15 cm. He leaves a margin of 2.5 cm at the top and bottom and 1.25 cm on either side. What percentage of paper area is approximately available for typing ?
(A) 60%
(B) 65%
(C) 70%
(D) 80%
Solution:
Area of the sheet = (30 × 15) cm2 = 450 cm2 Area used for typing = [(30 - 5) × (15 - 2.5)] cm2 = 312.5 cm2 ∴ Required percentage : $$\eqalign{ & = \left( {\frac{{312.5}}{{450}} \times 100} \right)\% \cr & = 69.4\% \approx 70\% \cr} $$
13.
The diameter of a circle is equal to the perimeter of a square whose area is 3136 cm2 . What is the circumference of the circle ?
(A) 352 cm
(B) 704 cm
(C) 39424 cm
(D) 1024 cm
Solution:
Area of square = 3136 cm2 Side of squared = $$\sqrt {3136} $$ = 56 cm Perimeter of square : = 4a = (4 × 56) cm = 224 cm = diameter of circle ∴ Circumference of circle : $$\eqalign{ & = \pi d \cr & = \frac{{22}}{7} \times 224 \cr & = 704{\text{ cm}} \cr} $$
14.
A coaching institute wants to execute tiling work for one of its teaching halls 60 m long and 40 m wide with a square tile of 0.4 m side. If each tile costs Rs. 5, the total cost of tiles would be :
(A) Rs. 60000
(B) Rs. 65000
(C) Rs. 70000
(D) Rs. 75000
Solution:
Number of tiles required : $$\eqalign{ & = \frac{{{\text{Area of hall}}}}{{{\text{Area of each tile}}}} \cr & = \left( {\frac{{60 \times 40}}{{0.4 \times 0.4}}} \right) \cr & = 15000 \cr} $$ ∴ Total cost of tiles : = Rs. (15000 × 5) = Rs. 75000
15.
A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq.ft per day, they approximately what time will be taken by the cow to graze the whole field ?
(A) 2 days
(B) 6 days
(C) 18 days
(D) 24 days
Solution:
Area of the field grazed : $$\eqalign{ & = \left( {\frac{{22}}{7} \times 14 \times 14} \right)sq.ft \cr & = 616\,sq.ft \cr} $$ Number of days taken to graze the field : $$\eqalign{ & = \frac{{616}}{{100}}\text{days} \cr & = 6\,\text{days}(\text{approx}) \cr} $$
16.
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 7803 sq. mtr, what is the breadth of the rectangular plot ?
(A) 51 m
(B) 88 m
(C) 104 m
(D) 153 m
Solution:
Let the breadth of the plot be x metres Then, length of the plot = (3x) metres x × 3x = 7803 ⇒ 3x2 = 7803 ⇒ x2 = 2601 ⇒ x = $$\sqrt {2601} $$ ⇒ x = 51 m
17.
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 2%
(B) 2.02%
(C) 4%
(D) 4.04%
Solution:
100 cm is read as 102 cm. ∴ A1 = (100 x 100) cm2 and A2 (102 x 102) cm2 (A2 - A1) = [(102)2 - (100)2] = (102 + 100) x (102 - 100) = 404 cm2 ∴ Percentage error $$\eqalign{ & = \left( {\frac{{404}}{{100 \times 100}} \times 100} \right)\% \cr & = 4.04\% \cr} $$
18.
The circumferences of two circle are 132 metres and 176 metres respectively. What is the difference between the area of the larger circle and the smaller circle ?