1. Rambabu can do a piece of work in 5 days and Santosh can do the same work in 7 days. If both work together, they will finish the work in how many days?

A. 12 days B. 2 days C. [latex] 2 \frac{11}{12}[/latex] D. [latex]\frac{12}{35}[/latex]

Answer - Option C
Explanation -
[latex]\frac{5 * 7}{5 + 7} = \frac{35}{12} = 2 \frac{11}{12}[/latex] days
2. A man goes from Delhi to Dehradun. Half the distance he covers by bus at an average speed of 50 km/hr and the other half by train at an average speed of 70 km/hr. The average speed for the whole journey was

A. 56 km/hr B. 64 km/hr C. 60 km/hr D. None of these

Answer - Option D
Explanation -
v - bar = [latex]\frac {2uv} {u + v}[/latex] = [latex]\frac {2 * 50 * 70} {50 + 70}[/latex] =[latex] 58 \frac {1} {3}[/latex]
3. Rakesh took a loan for 7 years at the rate of 6 % p.a. S.I. If total interest paid was Rs. 2100, then principal was

A. Rs. 4400 B. Rs. 4800 C. Rs. 5000 D. Rs. 5200

Answer - Option C
Explanation -
Principal = Rs[latex](\frac {2100 * 100} {7 * 6} )[/latex] = Rs. 500
4. How much should money lender lend at simple rate of interest of 15% in order to have Rs. 3234 at the end of [latex] 1 \frac {1} {2}[/latex] years

A. Rs. 1640 B. Rs. 2620 C. Rs. 2610 D. Rs. 2640

Answer - Option D
Explanation -
Let required money be x
Then [latex]( x + \frac {x * 15} {100} * \frac {3}{2}[/latex] = 3234
[latex]\frac {49 x} {40}[/latex] = 3234
i.e, x = [latex]\frac {3234 * 40} {49}[/latex] = 2640
5. Rajan buys lemons at the rate of 9 for 80p and sells them at 11 for 120p. His gain per lemon is

A. [latex]\frac {200} {99}[/latex] B. [latex]\frac {11} {99}[/latex] C. [latex]\frac {120} {99}[/latex] D. [latex]\frac {11} {9}[/latex]

Answer - Option A
Explanation -
CP = [latex]\frac {80} {9}[/latex]; SP = [latex]\frac {120} {11}[/latex]
i.e, Gain per lemon = [latex]\frac {120} {11} - \frac {80} {9} = \frac {200} {99}[/latex]
6. A man travels first 80 km at 20 kmph, next 30 km at 15 kmph and then 80 km at 20 kmph. His average speed for the whole journey (in kmph) is

A. 20 B. 22 C. 17 D. 19

Answer - Option D
Explanation -
Man travels total distance of 80 + 30 + 80 = 190 kilometers.
Times taken
for [latex]{1}^{st}[/latex] phase = [latex]\frac{80 km}{20 km/hr}[/latex] = 4hr
for [latex]{2}^{nd}[/latex] phase= [latex]\frac{30 km}{15 km/hr}[/latex] = 2hr
for [latex]{3}^{rd}[/latex] phase= [latex]\frac{80 km}{20 km/hr}[/latex] = 4hr
So, average speed for the whole journey
= [latex]\frac{Total dist ance}{Total time taken}[/latex]
= [latex]\frac{80 + 30 + 80}{4 + 2 + 4}hr[/latex] = [latex]\frac{190 km}{10 hr}[/latex] = 19 km/hr
7. A horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long. Over how much area of the field can it graze ?

A. 154 [latex] {m}^{2}[/latex] B. 308 [latex] {m}^{2}[/latex] C. 150 [latex] {m}^{2}[/latex] D. None of these

Answer - Option A
8. The difference between the local value and face value of 7 in the numeral 657903 is:

A. O B. 7896 C. 6993 D. 903

Answer - Option C
Explanation -
(Local value) - (Face value) = (7000 - 7) = 6993.
9. The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is:

A. 7 B. 29 C. 41 D. 67

Answer - Option D
Explanation -
x + (x + 36) + y = 100 [latex]\Rightarrow[/latex] 2x + y = 64
Therefore y must be even prime, which is 2.
Therefore 2x + 2 = 64 [latex]\Rightarrow[/latex] x = 31
Third prime number= (x + 36) = (31 + 36) = 67.
10. (51 + 52 + 53 +………+ 100) is equal to:

A. 2225 B. 3345 C. 3775 D. 3770

Answer - Option C
Explanation -
(51+52+53+………+100) = (1+2+3+…….+100)- (1+2+3+4+……+50)
= [latex]\frac {(100 \times 101)}{2}[/latex] - [latex]\frac {(50 \times 51)}{2}[/latex]
= (5050 - 1275)= 3775.