31 . 
Each interior angle of a regular polygon is 120° greater than each exterior angle. How many sides are there in the polygon? 

Answer & Explanation
Answer : Option
C


Explanation : 

Let an exterior angle $A^o$
Then each interior angle will be 120 + $A^o$
We know that in any regular polygon, the sum of an exterior and interior angle is always = $180^o$
A + 120 + A = 180 $\Rightarrow$ A = $30^o$
No. of sides of a polygon = $360 \over 30$ = 12 





32 . 
In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution, so that the resultant solution has 40% methyl alcohol in it? 

Answer & Explanation
Answer : Option
A


Explanation : 







33 . 
A, B and C can do a piece of work in 15 days. All three worked for 2 days and then A left. B and C worked for 10 more days and B left. C worked for another 40 days and completed the work. In how many days can A alone complete the work, if C can complete it in 75 days? 

Answer & Explanation
Answer : Option
A


Explanation : 

Assume the total work to be 600 units.
(LCM of all the numbers)
Then C's 1 day work = 8 units.
$\Rightarrow$(A + B + C)'s 1 day work = 40 units.
A, B, C work together in the first 2 days
$\Rightarrow$Work done in the first 2 days
= 40 $\times$ 2 = 80 units
C alone works during the last 40 days
$\Rightarrow$Work done in the last 40 days
= 40 $\times$ 8 = 320 units
Remaining work = 600  (320 + 80)
= 200 units
This work is done by B and C in 10 days.
$\Rightarrow$(B + C)'s 1 day work = 20 units
$\Rightarrow$A's 1 day work = (A + B + C)'s 1 day work 
(B + C)'s 1 day work = 40 units  20 units =
20 units
$\Rightarrow$A can do the work of 600 units in $600\over 20$
= 30 days 





34 . 
A tower standing on a horizontal plain subtends a certain angle at a point 160 m apart from the foot of the tower. On moving 100 m towards the tower, it is found that the subtended angle is now twice as before. What will be twice the length of the height of the tower? 

Answer & Explanation
Answer : Option
B


Explanation : 







35 . 
If $2x^2 + 5 x + 1 \over 5x$ = 3, then $2x \over 2x^2 + 1$ = ? 

Answer & Explanation
Answer : Option
C


Explanation : 







36 . 
The average age of a college is 21.8 years. The average age of students of college is 24.2 years and average age of lecturers of college is 20.6 years. Find the ratio of the number of students to that of lecturers? 

Answer & Explanation
Answer : Option
D


Explanation : 







37 . 
A man and a woman 81 miles apart from each other, start travelling towards each other at the same time. If the man covers 5 m/hr to the women's 4 m/hr, how far would the woman have travelled when they meet? 

Answer & Explanation
Answer : Option
B


Explanation : 

Time taken to meet = $Distance\,\,\, between \,\,\,them\over Relative \,\,\,speed$
= $81 \over (4 + 5)$ = 9 hrs
Distance traveled by women = 9 $\times$ 4
= 36 miles 





38 . 
Find the total surface area of the pyramid with base length and height be 10 cm and 12 cm respectively 

Answer & Explanation
Answer : Option
B


Explanation : 







39 . 
If x + $2\over x$ = 1. then $x^2 + x + 2 \over x^2 (1  x)$ = ? 

Answer & Explanation
Answer : Option
C


Explanation : 







40 . 
A wheel of a car of radius 21 cm is rotating at 600 RPM. What is the speed of the car in km/hr? 

Answer & Explanation
Answer : Option
B


Explanation : 

The radius of the wheel measures 21 cm.
In one rotation this wheel will cover
= 2 $\times$ $\pi$ $\times$ 21 = 132 cm.
In an hour, the wheel will cover a distance of (132 $\times$ 600) $\times$ 60 = 4752000 cm.
The speed of the car = 4752000 cm/hr
= 47.52 km/hr 





41 . 
Peter invested a certain sum of money on simple interest whose value grew to Rs. 300 at the end of 3 years and to '400 at the end of another 5 years. What was the rate of interest in which he invested his sum? 

Answer & Explanation
Answer : Option
C


Explanation : 

The interest earned for the 5 year period between the 3rd year and 8th year
= 400  300 = 100
As the simple interest earned for a period of 5 years is 100, interest earned per year = 20
Interest earned for 3 years = 3 $\times$ 20 = 60.
Hence, initial amount invested = Amount after 3 years  Interest for 3 years
= 300  60 = 240
Rate of interest = $20 \over 240$ $\times$ 100 = 8.33 % 





42 . 
I travel the first part of my journey at 40 km/h and the second part at 60 km/h and cover the total distance of 240 km to reach my destination in 5 hr. How long did the first part of my journey last? 

Answer & Explanation
Answer : Option
B


Explanation : 

The total time of journey = 5 hours.
Let x hours be the time that I travelled at 40 km/h
5  xhrs would be time that I travelled at 60 km/h.
Now, we have
40x+ (5  x) $\times$ 60 = 240, we get
40x+ 300  60x= 240
20x= 60 or x= 3 hrs
We can say that the first part of journey last for 3 hrs 





43 . 
If $sec q + tan q \over sec q  tan q$ = $5 \over 3$, then sin 6$\sqrt{39}$ is 

Answer & Explanation
Answer : Option
C


Explanation : 







44 . 
A trader buys goods at a 19% discount on the label price. If he wants to make a profit of 20% after allowing a discount of 10%, by what % should his marked price be greater than the original label price? 

Answer & Explanation
Answer : Option
D


Explanation : 

Let the label price be = Rs.100. The trader buys at a discount of 19%.
Hence, his cost = 100  19 = 81.
He wants to make a profit of 20%. Hence his selling price = 1.2 (81) = 97.2
However, he wants to get this Rs/ 97.2 after providing for a discount of 10%. i.e. he will be selling at 90% of his marked price.
Hence, his marked price = 108 which is 8% morethan the original label price. 





45 . 
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm and 12 m 95 cm is: 

Answer & Explanation
Answer : Option
A


Explanation : 

Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm 





