1. The average of first, second and third number was 40. The average of second, third and fourth number was 41, and fourth number was 45. Find the first number.
1) 39
2) 40
3) 43
4) 42
5) 47

2. A certain sum is interested at compound rate. The interest accrued in the first two year is Rs. 544 and that in the first three years is Rs. 868. Find the rate percent.
1) 13 1/2%
2) 9%
3) 17%
4) 14%
5) 12 1/2%

3. 50 gm of an alloy of gold and silver contains 80% gold (by weight). Find the quantity of gold that is to be mixed up with this alloy so that it may contain 95% gold.
1) 146 gm
2) 150 gm
3) 147 gm
4) 156 gm
5) 153 gm

4. A team of 80 men is supposed to do a work in 64 days. After 36 days, 20 more men were employed and the work finished 2 days earlier. How many days would it have been delayed if 20 more men were not employed?
1) 4 1/2 days
2) 5 1/4 days
3) 6 days
4) 3 1/3 days
5) 4 1/4 days

5. Two trains x and y start from Delhi and Ranchi towards Ranchi and Delhi respectively. After passing each other they take 6 hours 40 minutes and 3 hours 45 minutes to reach Ranchi and Delhi respectively. If the train from Delhi is moving at 60 km/hr then find the speed of other train.
1) 78 km/hr
2) 72 km/hr
3) 83 km/hr
4) 80 km/hr
5) 68 km/hr

6. A man can row 12 km/hr in still water. If the river is running at 4 km/hr, it takes 5 hours more in upstream than to go downstream for the same distance. How far is the place?
1) 76 km
2) 80 km
3) 75 km
4) 82 km
5) 84 km

7. A lawn is in the form of a rectangle and length is one and half as long as it is broad. The area of the lawn is 3/2 hectares. The length of the lawn is:
1) 150 m
2) 162 m
3) 153 m
4) 147 m
5) 138 m

8. The sum of length, breadth and height of a cuboid is 24 cm and its diagonal is 18 cm long. Find the total surface area of the cuboid.
1) 273 cm^2
2) 252 cm^2
3) 217 cm^2
4) 290 cm^2
5) 187 cm^2

9. In how many ways 4 boys and 4 girls can be seated in a row so that boys and girls are alternate?
1) 1152
2) 1211
3) 1052
4) 1202
5) 977

1.4
First number = 40 × 3 – (41 × 3 – 45)
= 120 – 123 + 45 = 42

2. 5
P[(1 + R/100)^3 - 1] = 868 --- (I)
P[(1 + R/100)^2 - 1] = 544 --- (II)

Divinding eq I by II and put, q = 1 + r/100
(q^3 - 1)/(q^2 - 1) = 868/544
[(q - 1)(q^2 + q + 1)]/(q - 1)(q + 1) = 217/136
(q^2 + q + 1)/(q + 1) = 217/136
q^2/q+1 = 81/136
136q^2 - 81q - 81
q = 9/8
1 + r/100 = 9/8
r = 1/8 * 100% = 12 1/2%

3. 2
Quantity of gold to be added
50 (95-80)/(100-95) = 50*15/5 = 150 gm

4. 1
Required answer
= [y{D - (d1 + d2)} - d2x]/ x
Where
y = 20
x = 80
D = 64
d1 = 36
d2 = 2
= [20{64 - (36 + 2)} - 2 * 80]/80
= (20 * 26 - 160)/80
(520 - 160)/80 = 4 1/2days

5. 4
Speed of other train = 60 sqroot[(6 2/3 / 3 3/4)]
= 60 sqroot[(20/3 * 3 4/15)]
= 60 * 4/3
= 80 km/hr

6. 2
Let the distance be x km
x/12-4 - x/12 + 4 = 5
x = 80km

7. 1
Let breadth = x m and length = 3/2 km
x * 3/2x = 3/2 * 10000
x^2 = 10000
x = 100 m
Length = 3/2 * 100 = 150m

8. 2
Total surface area = (sum of all three sides)2 – (Diagonal)2
= (24)^2 – (18)^2
= 42 × 6 = 252 cm^2

9. 1
Required number of ways = 2 × 4! × 4! = 1152