*560*

**1. A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?**

A. 1 / 3

B. 1 / 4

C. 1 / 5

D. 1 / 7

Ex:Suppose the vessel initially contains 8 litres of liquid. Let x littres of this liquid be replaced with water.

Quantity of water in new mixture = (3 – 3x/8 + x) litres.

Quantity of syrup in new mixture = (5 – 5x/8) litres.

(3 – 3x/8 + x) = (5 – 5x/8) = 5x + 24 = 40 – 5x

=› 10x = 16 =› x = 8/5

So, part of the mixture replaced = (8/5 x 1/8) = 1/5.

**2. The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field?**

A. 18750 sq.m

B. 37500 sq.m

C. 40000 sq.m

D. 48000 sq.m

Ex:So length =250 m;breadth=150 m

Area = (250 x 150)m²

= 37500 m²

**3. A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?**

A. 19

B. 29

C. 39

D. 49

Ex:Let the average after 17th inning = x. Then, average after 16th inning = (x – 3)

Average=16 (x-3)+87

= 17x or x=(87-48)

= 39.

**4. The banker’s discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?**

A. 3 months

B. 4 months

C. 5 months

D. 6 months

EX:S.I on Rs.1800 = T.D on Rs.1872.

P.W on Rs.1872 is Rs.1800.

Rs.72 is S.I on Rs. 1800 at 12%.

Time =(100×72 / 12×1800)

= 1/3 year

= 4 months.

**5. A boat can travel with a speed of 13 km / hr in still water. If the speed of the stream is 4 km / hr. find the time taken by the boat to go 68 km downstream?**

A. 2 hours

B. 3 hours

C. 4 hours

D. 5 hours

Ex:Speed Downstream= (13 + 4) km/hr

= 17 km/hr.

Time taken to travel 68 km downstream =(68 / 17)hrs

= 4 hrs.

**6. An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?**

A. 144°

B. 150°

C. 168°

D. 180°

Ex:Angle traced by hour hand in

5 hrs 10 min. = (360/12 x 6)°

= 180°.

**7. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is**

A. Rs. 1550

B. Rs. 1650

C. Rs. 1750

D. Rs. 2000

Ex:C.I. =Rs[4000x(1+10/100)²-4000]

Rs.(4000×11/10×11/10-4000)= Rs.940.

Sum=Rs. [420×100 /3×8]

= Rs.1750.

**8. (7.5×7.5+3.75+2.5×2.5) is equal to**

A. 30

B. 60

C. 80

D. 100

Ex:Given expression= (7.5×7.5+2×7.5×2.5+2.5×2.5)²

= (a²+2ab+b²)

=(a+b)²

= (7.5+2.5)²

= 10²

= 100.

**9. The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree**

A. 30°

B. 45°

C. 60°

D. 90°

EX:Let AB be the tree and AC be its shadow.

Then, < ABC= θ.

Then, AC/AB= √3

cotθ= √3

θ=30°

**10. If log 2 = 0.30103, the number of digits in 520 is**

A. 14

B. 16

C. 18

D. 25

Ex:Log 520=20 log 5

=20 ×[log(10/2)]

=20 (log 10 – log 2)

=20 (1 – 0.3010)

=20×0.6990

=13.9800.

Characteristics = 13.

Hence, the number of digits in Log 520 is 14.