16th May: Quantitative Aptitude Quiz for NIACL and SBI PO Mains

Quantitative Aptitude Quiz for NIACL and SBI PO Mains
1. The ages of P, Q and R form an arithmetic progression. After 5 years, the ratio of ages of Q and R will be 6 : 7. Difference between ages of P and Q is 6 years. What was P’s age 3 years back?
A) 20 years
B) 21 years
C) 22 years
D) 24 years
E) 23 years
2. Harry and Benny invested a total of Rs. 30000 in compound interest for 2 years. Harry invested at 15% per annum while Benny at 10% per annum. The total interest generated at the end of 2 years was Rs. 8662.5. What was the share of Benny in the investment (in rupees)?
A) 12000
B) 15000
C) 9000
D) 13000
E) 16000
3. A spherical lump of Copper of radius 3 cm is taken and drawn into wire of diameter 0.6 mm. What is the maximum length of wire that can be formed? (Use π = 3.14)
A) 4 metres
B) 1200 metres
C) 12 metres
D) 400 metres
E) 628 metres
4. In a mixture of oil and water, the weight of oil is twice that of water. Also, the density of water is twice that of oil. Another mixture of oil and water have 2 kg oil and 2 kg water. Both are mixed together and it is found that the ratio of weights of oil and water in mixture is 17:9. What was the weight of first mixture?
A) 24 kg
B) 36 kg
C) 44 kg
D) 48 kg
E) 50 kg
5. P and Q bought a carpet each for Rs. 600. P sold his carpet to R at 10% profit, while Q sold his carpet to S at 15% loss. Now, R sold the carpet to S at 10% loss. For how much did S bought the two carpets in total?
A) Rs. 1100
B) Rs. 1050
C) Rs. 1104
D) Rs. 1140
E) Rs. 1144
6. A train runs at a speed of 45 km/hr. It can cross a platform of length 400 metres in 40 seconds. By how much should it increase its speed so as to cross a bridge of length 500 metres in 30 seconds (in m/sec)?
A) 7.5
B) 10
C) 12.5
D) 15
E) 20
7. P, Q and R can finish a work in 12 hours, 20 hours and 24 hours, respectively, when working alone. P starts the work and works for an hour. Then, Q joins him. After another 2 hours, R joins them. In how many hours, will the work gets finished?
A) 5
B) 6
C) 43/7
D) 47/7
E) 7
8. A and B started a business by investing Rs 20,000 and Rs 25,000 respectively.  After 4 months B left and C joined by investing Rs 15,000. At the end of year, there was a profit of Rs 23,000, find the share of C in the profit.
A) Rs. 5500
B) Rs. 6000
C) Rs. 5000
D) Rs. 7500
E) None of these
9. The average salary per head of all the workers in a company is Rs. 90. The average salary of 12 officers is Rs. 520 and the average salary per head of the rest is Rs. 80. Find the total number of workers in the workshop.
A) 660
B) 880
C) 650
D) 460
E) 528
10. A biased coin is tossed 4 times. The probability that a head occurs when this coin is tossed is 0.25. What is the probability that exactly 2 tails occur?
A) 0.21
B) 0.64
C) 0.27
D) 0.43
E) 0.5
Solutions:
1. C) The ages of P, Q and R form an arithmetic progression. Difference between ages of P and Q is 6 years. So, difference between ages of Q and R would also be 6 years.
Let age of Q be T years, and that of R be (T + 6) years.
After 5 years, the ratio of ages of Q and R will be 6 : 7.
(T + 5)/(T + 11) = 6/7
7T + 35 = 6T + 66
T = 31
Age of Q = 31 years
Age of P = 6 years lesser than age of Q = 25 years
3 years back, age of P was 22 years.
2. C) 3. D) Let the maximum length of wire that can be drawn is L cm.
Radius of wire = 0.6 mm/2 = 0.3 mm = 0.03 cm
Volume of Copper will be same in both cases. Shape of wire is cylindrical.
Volume of sphere = Volume of cylinder
(4/3) × 3.14 × 3 × 3 × 3 = 3.14 × 0.03 × 0.03 × L
L = 40000
Maximum length of wire that can be drawn = 40000 cm = 400 metres
4. D) Let T kg of first mixture is taken. In it, the weight of oil is twice that of water, means ratio of their weights is 2 : 1.
Weight of oil in first mixture = 2/(2 + 1) × T = 2T/3 kg
Weight of water in first mixture = 1/(2 + 1) × T = T/3 kg
Ratio of weights of oil and water in mixture => [(2T/3 + 2)]/[(T/3 + 2)] = 17/9
=> 18T/3 + 18 = 17T/3 + 34 => T/3 = 16 => T = 48
Therefore weight of the first mixture taken is 48kg.
5. C) P sold his carpet to R at 10% profit.
We know, Selling price = Cost Price × (1 + (Profit %)/100)
Cost price for R = Selling price for P = Rs. 600 × (1+10/100) = Rs. 660
Then, R sold the carpet to S at 10% loss.
We know, Selling price = Cost Price × (1 – (Loss %)/100)
Cost price for S for first carpet = Selling price for R = Rs. 660 × (1 – 10/100) = Rs. 594
Q sold his carpet to S at 15% loss.
Cost price for S for second carpet = Selling price for Q = Rs. 600 × (1 – 15/100) = Rs. 510
Price at which S bought the two carpets = Rs. 594 + Rs. 510 = Rs. 1104
6. A) Speed of train = 45 km/hr = 45 × (5/18) m/sec = 12.5 m/sec
Let length of train be N metres.
Time taken to cross platform = (length of train + length of platform)/speed of train
40 = (N + 400)/12.5
N = 500 400 = 100
Length of train is 100 metres.
Suppose train increases its speed by T m/sec.
Time taken to cross bridge = (length of train + length of bridge)/speed of train
30 = (100 + 500)/(12.5 + T)
375 + 30T = 600
T = 225/30 = 7.5
Speed should be increased by 7.5 m/sec.
7. D) P, Q and R can finish a work in 12 hours, 20 hours and 24 hours, respectively, when working alone.
In one hour, P, Q and R can finish 1/12, 1/20 and 1/24 of work, respectively.
Suppose work gets finished in T hours.
P starts the work and works for an hour. Then, Q joins him. After another 2 hours, R joins them.
P worked for T hours, Q worked for (T 1) hours and R worked for (T 3) hours. 8. B) According to the law of partnership:
A’s share : B’s share : C’s share
= (20,000 × 12) : (25,000 × 4) : (15,000 × 8)
= 240,000 : 100,000 : 120,000
= 12 : 5 : 6
Now, let the shares of A, B and C are 12x, 5x and 6x respectively, then
12x + 5x + 6x = 23,000
23x = 23,000
x = 1000
Share of C = 6x = 6 × 1000
= Rs 6000
Hence, the required answer is Rs 6000.
9. E) Let the number of workers be x.
The average salary per head of all the workers in a company is Rs. 90.
So, the sum of salary of all the workers in the company = Rs. 90x
The average salary of 12 officers is Rs. 520.
So, the total salary of 12 officers = Rs. (520 × 12) = Rs. 6240
The average salary per head of the rest is Rs. 80.
Number of remaining workers = (x – 12)
Then, total salary of the remaining workers = Rs. [80 × (x – 12)]
We can write, 6240 + [80 × (x - 12)] = 90x
6240 + 80x - 960 = 90x
90x 80x = 5280
10x = 5280
x = 5280/10 = 528
The number of total workers in the company is 528.
10. A) The probability that a heads occurs when this coin is tossed is 0.25.
Probability of occurrence of tails = 1 0.25 = 0.75
For exactly two tails to occur in 4 tosses, remaining two outcomes should be heads.
In 4 tosses, 2 tails can occur in 4C2 ways, i.e., 6 ways.
Probability of exactly 2 tails = 6 × 0.75 × 0.75 × 0.25 × 0.25 = 0.21