Mock Test 3 Arithmetic Questions with Explanations
 If 3√5 + √125 = 17.88, then what will be the value of √80 + 6√5 ?
Explanation:
3√5 + √125 = 17.88
3√5 + √25 x 5 = 17.88
3√5 + 5√5 = 17.88
8√5 = 17.88
√5 = 2.235
√80 + 6√5 = √16 x 5 + 6√5
= 4√5 + 6√5
= 10√5 = (10 x 2.235) = 22.35
2. A man has Rs. 480 in the denominations of onerupee notes, fiverupee notes and tenrupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Explanation:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
3. It is being given that (2^{32} + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Explanation:
Let 2^{32} = x. Then, (2^{32} + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(2^{96} + 1) = [(2^{32})^{3} + 1] = (x^{3} + 1) = (x + 1)(x^{2} – x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
4. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
Explanation:
Ratio of times taken by A and B = 1 : 3.
The time difference is (3 – 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes  3  x 60  = 90 days.  
2 
So, A takes 30 days to do the work.
A’s 1 day’s work =  1 
30 
B’s 1 day’s work =  1 
90 
(A + B)’s 1 day’s work =  1  +  1  =  4  =  2  
30  90  90  45 
A and B together can do the work in  45  = 22  1  days. 
2  2 
5. If selling price is doubled, the profit triples. Find the profit percent.
Explanation:
Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y – x) = (2y – x) y = 2x.
Profit = Rs. (y – x) = Rs. (2x – x) = Rs. x.
Profit % =  x  x 100  % = 100%  
x 
6. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R =  100 x 60  = 10% p.a.  
100 x 6 
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
C.I. 




= 3972. 
7. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Explanation:
Perimeter = Distance covered in 8 min. =  12000  x 8  m = 1600 m.  
60 
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m^{2} = 153600 m^{2}.