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Q:

A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is

A) rs.58	B) rs.158
C) rs.258	D) rs.358

Answer & Explanation Answer: C) rs.258

Explanation:

area of cross roads = (55 x 4) + (35 x 4)- (4 x 4) = 344sq m

cost of graveling = 344 x (75/100) = Rs. 258

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Q:

The area of a field in the shape of a trapezium measures 1440sq m. The perpendicular distance between its parallel sides is 24cm. If the ratio of the sides is 5:3, the length of the longer parallel side is:

A) 75	B) 85
C) 95	D) 105

Answer & Explanation Answer: A) 75

Explanation:

Area of field = $\frac{1}{2} * (5 x + 3 x) * 24$ = 96x sq.m

96x = 1440 => x = $\frac{1440}{96}$ = 15

Hence, the length of longer parallel side = 5x = 75m

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Q:

If a parallelogram with area p, a triangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then

A) P=R	B) P=A
C) P=A/2	D) P=2R

Answer & Explanation Answer: A) P=R

Explanation:

let each have base = b and height = h
then p = b*h, R = b*h and T = (1/2) * b*h
so P = R, P = 2T and T = (1/2)*R are all correct statements

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Q:

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

A) 136	B) 236
C) 336	D) 436

Answer & Explanation Answer: C) 336

Explanation:

let ABCD be the given parallelogram

area of parallelogram ABCD = 2 x (area of triangle ABC)

now a = 30m, b = 14m and c = 40m

s=1/2 x (30+14+40) = 42

Area of triangle ABC = $\sqrt{[s (s - a) (s - b) (s - c)]}$

= $\sqrt{[42 (12) (28) (2)]}$ = 168sq m

area of parallelogram ABCD = 2 x 168 = 336 sq m

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Q:

The difference between two parallel sides of a trapezium is 4 cm. perpendicular distance between them is 19 cm. If the area of the trapezium is 475 find the lengths of the parallel sides.

A) 27 and 23	B) 24 and 23
C) 25 and 23	D) 22 and 23

Answer & Explanation Answer: A) 27 and 23

Explanation:

Let the two parallel sides of the trapezium be a cm and b cm.

Then, a - b = 4

And, $\frac{1}{2} \times (a + b) \times 19 = 475 = > (a + b) = 50$

Solving (i) and (ii), we get: a = 27, b = 23.

So, the two parallel sides are 27 cm and 23 cm.

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Q:

The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height

A) 6	B) 7
C) 8	D) 9

Answer & Explanation Answer: A) 6

Explanation:

Let the height of the parallelogram be x. cm. Then, base = (2x) cm.

$2 x \times x = 72 = > 2 x^{2} = 72 = > x = 6$

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Q:

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

A) 9	B) 9.6
C) 10	D) 10.8

Answer & Explanation Answer: D) 10.8

Explanation:

Relative speed = (60 + 40) km/hr =[ 100 x ( 5 / 18 ) ]m/sec = ( 250 /9 ) m/sec.
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = [ 300 x ( 9/250 ) ] sec = ( 54/ 5 )sec = 10.8 sec.

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