1. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
A. 14 years
B. 18 years
C. 20 years
D. 22 years
Answer: Option D
Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
2. The square root of 64009 is:
A. 253
B. 347
C. 363
D. 803
Answer: Option A
Explanation:
2|64009( 253
|4
|----------
45|240
|225
|----------
503| 1509
| 1509
|----------
| X
|----------
[latex]\sqrt{64009}[/latex] = 253.
3. A man invested Rs. 1552 in stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
A. 7.5%
B. 8%
C. 9.7%
D. None of these
Answer: Option B
Explanation:
By investing Rs. 1552, income = Rs. 128.
By investing Rs. 97, income = Rs. ([latex]\frac{128}{1552}[/latex] x 97 ) = Rs. 8.
Dividend = 8%
4. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R are Rs. 5200. The monthly income of P is:
A. 3500
B. 4000
C. 4050
D. 5000
Answer: Option B
Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000.
P's monthly income = Rs. 4000.
5. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
A. [latex]\frac{1}{10}[/latex]
B. [latex]\frac{2}{5}[/latex]
C. [latex]\frac{2}{7}[/latex]
D. [latex]\frac{5}{7}[/latex]
Answer: Option C
Explanation:
P (getting a prize) = [latex]\frac{10}{10 + 25}[/latex] = [latex]\frac{10}{35}[/latex] = [latex]\frac{2}{7}[/latex].
6. A sum of Rs. 725 is lent at the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
A. 3.6%
B. 4.5%
C. 5%
D. 6%
E. None of these
Answer: Option E
Explanation:
Let the original rate be R%. Then, new rate = (2R)%.
Note:
Here, the original rate is for 1 year(s); the new rate is for only 4 months i.e. [latex]\frac {1}{3}[/latex] year(s).
([latex]\frac {725 \times R \times 1}{100}[/latex] ) + ([latex]\frac {362.50 \times 2R \times 1}{100 \times 3}[/latex]) = 33.50
(2175 + 725) R = 33.50 x 100 x 3
(2175 + 725) R = 10050
(2900)R = 10050
R = [latex]\frac {10050}{2900}[/latex] = 3.46
Original rate = 3.46%
7. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
A. 49 m[latex]^{2}[/latex]
B. 50 m[latex]^{2}[/latex]
C. 53.5 m[latex]^{2}[/latex]
D. 55 m[latex]^{2}[/latex]
Answer: Option A
Explanation:
Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m[latex]^{2}[/latex]
= 49 m[latex]^{2}[/latex].
8. If log[latex]_{10}[/latex] 2 = 0.3010, then log[latex]_{2}[/latex] 10 is equal to:
A. [latex]\frac {699}{301}[/latex]
B. [latex]\frac {1000}{301}[/latex]
C. 0.3010
D. 0.6990
Answer: Option B
Explanation:
log[latex]_{2}[/latex] 10 = [latex]\frac {1}{log_{10} 2}[/latex] = [latex]\frac {1}{0.3010}[/latex] = [latex]\frac {10000}{3010}[/latex] = [latex]\frac {1000}{301}[/latex].
9. In a 200 meters race A beats B by 35 m or 7 seconds. A's time over the course is:
A. 40 sec
B. 47 sec
C. 33 sec
D. None of these
Answer: Option C
Explanation:
B runs 35 m in 7 sec.
B covers 200 m in ([latex]\frac {7}{35}[/latex] x 200) = 40 sec.
B's time over the course = 40 sec.
A's time over the course (40 - 7) sec = 33 sec.
10. The price of 2 sarees and 4 shirts is Rs. 1600. With the same money, one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay?
A. Rs. 1200
B. Rs. 2400
C. Rs. 4800
D. Cannot be determined
E. None of these
Answer: Option B
Explanation:
Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply the value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
11. 18 men bind 900 books in 10 days. Find how many binders will be required to bind 600 books in 12 days?
Answer: Option A
Explanation:
We have to find the number of binders. Let the number of binders be x.
Direct Proportion:Less Books (↓),Less binders(↓)
Indirect Proportion:More days (↑),Less binders (↓)
\[ 18 : x ::
\begin{cases}
900 : 600 - - - (Books) \\
12 : 10 - - - (Days)
\end{cases}
\]
x × 900 × 12 = 18 × 600 × 10
x = [latex]\frac {18 \times 600 \times 10}{900 \times 12}[/latex] = 10
12. (1331)[latex]^{- (2/3)}[/latex]
A. –[latex]\frac {1}{11}[/latex]
B. – [latex]\frac {11}{121}[/latex]
C. [latex]\frac {1}{122}[/latex]
D. [latex]\frac {121}{11}[/latex]
Answer: Option C
Explanation:
Cube root of 1331 is 11. Therefore,
(11)[latex]^{3 \times -(2/3)}[/latex]
Remember the law of indices (xm)n = xmn
(11)[latex]^{3 \times -(2/3)}[/latex] = 11[latex]^{-2}[/latex]
x[latex]^{-1}[/latex] = [latex]\frac {1}{x}[/latex]
Hence, 11[latex]^{-2}[/latex] = [latex]\frac {1}{112}[/latex] = [latex]\frac {1}{112}[/latex]
13. There is a road besides a river. Two friends Ram & Shyam started their journey from place P, moved to the garden located at another place Q & then returned to place P. Ram moves by swimming at a speed of 15 km/hr while Shyam sails on a boat at a speed of about 12 km/hr. If the flow of water current is at the speed of 6 km/hr, what will be the average speed of boat sailor?
A. 6 km/hr
B. 9 km/hr
C. 12 km/hr
D. 18 km/hr
Answer: Option B
Explanation:
Average Speed =[latex]\frac {Downstream Speed \times Upstream Speed}{Speed in still water}[/latex]
=[latex]\frac {(x + y) (x – y)}{x}[/latex]km/hr
Speed of boat in still water = y [latex]\frac {(t2 + t1)}{(t2 – t1)}[/latex]km/hr
As Ram swims both the ways at the speed of 15 km/hr, the average speed of swimming is 15 km/hr.
Being a boat sailor, Shyam moves downstream at speed = 12 + 6 = 18 km/hr & upstream at speed = 12 – 6 = 6 km/hr
Therefore, average speed of boat sailor = Downstream speed x Upstream speed / speed in still water
=[latex]\frac {[Downstream Speed \times Upstream Speed]}{[(1/2) \times ([Downstream Speed + Upstream Speed])]}[/latex]
=[latex]\frac {(18 \times 6)}{[(1/2) \times (18 + 6)]}[/latex]
=[latex]\frac {2 \times 18 \times 6}{18 + 6}[/latex]
= 9 km/hr
15. The remainder is 29, when a number is divided 56. If the same number is divided by 8, then what is the remainder?
Answer: Option D
Explanation:
We know that,
Dividend = [(Divisor × Quotient)] + Remainder
It is given that, the remainder is 29, when a number (dividend) is divided 56(divisor).
Dividend and quotient are unknown, hence assume dividend as X and quotient as Y.
Therefore,
X = 56 × Y + 29
56 is completely divisible by 8, but 29 is not completely divisible and we get remainder as 5, which is the required answer.
OR
X = 56 × Y + 29
= (8 × 7Y) + (8 × 3) + 5
5 is the required remainder.
3. Smith and Kate started a business investing Rs. 84,000 and Rs. 28,000 respectively. In what ratio the profit earned after 2 years be divided between Smith and Kate respectively?
A. 2 : 3
B. 3 : 1
C. 13 : 3
D. None of these
Answer: Option B
Explanation:
P’s share of profit = [latex]\frac {x}{y}[/latex] - - - - - - (x and y are investments)
Q’s share of profit
x : y = P’s share of profit : Q’s share of profit
Therefore,
[latex]\frac {Smith’s share of profit}{Smita’s share of profit}[/latex] = [latex]\frac {84000}{28000}[/latex] =[latex]\frac {3}{1}[/latex]
The profit earned after 2 years will be divided between Smith and Kate in the ratio of 3: 1.
Introduction