# Quantitative Aptitude Quiz for NIACL Mains

Quantitative Aptitude Quiz for NIACL Mains
1. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?
A) Rs.93,300
B) Rs.93,200
C) Rs.94,300
D) Rs.94,200
E) None of these
2. If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68 and if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P?
A) 17 years
B) 16 years
C) 15 years
D) 13 years
E) 12 years
3. Two taps A and B can fill a cistern in 12 min and 15 min respectively. They are opened together but after a few min, A is turned off and the rest of the cistern is filled by B in 5 min. After how many minutes was A turned off?
A) 4 min
B) 7 min
C) 6 min
D) 5 min
E) None of these
4. A sum of Rs. 30600 is divided between Richa and Atish, who are respectively 18 and 19 yr old, in such a way that if their shares are invested at 4% per annum compounded annually, they shall receive the same amount on reaching 21 yr of age. What is the share of Richa?
A) Rs.15000
B) Rs.16000
C) Rs.14000
D) Rs.15600
E) Rs.14500
5. A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The approximate percentage reduction in number of sheets is closest to
A) 5
B) 10
C) 15
D) 20
E) 25
6. The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the Praja Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time. How many voted for the Praja Party in the Assembly Elections.
A) 1,10,000
B) 1,20,000
C) 1,30,000
D) 1,40,000
E) 1,50,000
7. Two liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?
A) 2 : 3
B) 2 : 5
C) 3 : 4
D) 3 : 5
E) 2 : 1
8. Richa wanted to sell her two chairs that cost her a total of Rs. 545. She sold both the chairs. On selling one chair, she got 15% profit but she also generated a loss 12% on the other one. She did not get any profit and any loss in the whole transaction so. What is the cost price of the chair that she sold for a profit?
A) Rs.245
B) Rs.232
C) Rs.263
D) Rs.242
E) Rs.236
9. Meera invested some money in Local Community and obtained a profit of 6%. She again invested her money but this time she generated a loss of 9% on this transaction. If the investment of money was in the ratio of 2:3, then what is the loss percentage in the whole transaction?
A) 3%
B) 4%
C) 5%
D) 12%
E) 16%
10. Meera went to a Laptop shop. The cash price of laptop was Rs. 24945. She paid Rs. 3945 and gave the rest of money in two equal annual instalments. If the rate of interest is 5% compounded annually then what was the value of each installment?
A) Rs.11292.72
B) Rs.11293.90
C) Rs.11296.20
D) Rs.11295.00
E) Rs.11298.72
Solutions:
1. A) From the given data
The amount of money given to X = 12 × 300 + 12 × 330 + ... + 12 × 570
= 12[300 + 330 + ... + 540 + 570]
= 12 ×10/2[600 + 9 x 30 ] = 52200
Amount of money given to Y is 6 × 200 + 6 × 215 + 6 × 230 + 6 × 245 + ... to 20 terms
= 6[200 + 215 + 280 ... 485]
= 6 × 20/2[400 + 19 x 15]
= 6 × 10[400 + 285]
= 60 × 685 = 41100
Therefore Total amount paid = 52200 + 41100 = Rs. 93,300.
2. E) From the given conditions we can say that 2Q +P +R = 59 ………(1)
Q + R + 3P = 68  …………(2)
P +3Q +3R = 108 ………(3)
From (1), (2) and (3)
3Q + 3R + 9P = 204
P +3Q +3R = 108
So therefore 8P= 96 = P = 12
3. E) Let the turn off time of A = p min
Now we have case when the pipe was closed: we know that for the last 5 min B worked alone
hence 5/15 = 1/3rd of the tank is filled by b alone
If 1/3rd of the tank is filled by B alone,
then 2/3rd of the tank is filled by A & B together
A and B can full the tank in 1/12+1/15 = 9/60 = 1/ T
That means in 20/3 A and B can full the complete tank
Hence for the time for which A is on = 2/3 rd of the tank filled = 2/3 * 20/3 = 40/9 = 4 4/9
4. A) Let the share of Richa is p
Then the share of Atish is (30600 – p)
Therefore p x (1+4/100)3 =(30600 – p)(1+4/100)2
p x 104/100 = 30500 –p
p x 104/100 + p = 30500
(204/100)p = 30600
p = Rs.15000
5. D) Total volume of first report = (20 x 55 x 65) = 71500
Let n be the number of pages.
Therefore, the new volume will be = (65 x 70 x n) = 4550n
As the volume remains same, we can say that
71500 = 4550n
n = 15.71 = 16 sheets.
Clearly, the sheet reduced by 4 and percentage reduction in number of sheets =(4/20) x 100 = 20%.
6. D) Let the number of votes in the previous polls = n
So, the number of votes not cast for the party would be = 1.25n.
Total numbers of votes are 260000
Therefore, the number of votes cast in the two polls would be = (260000 – x) and (260000 – 1.25x)
Majority of votes in the previous polls = (votes cast) – (votes not cast) = (260000 – x) – x = (260000 – 2x).
Majority of votes lost in this year’s polls
= (votes not cast) – (votes cast) =1.25x – (260000 – 1.25x)
= (2.5x – 260000). According to the question
(Margin of loss this year) = 2 x (Margin of victory last year).
(2.5x – 260000) = 2(260000 – 2x).
Solving this equation we get,
x = 120000.
The number of votes not casted for the party in the previous assembly polls = 12000.
So, the number of votes casted for the party = (260000 – 120000) = 140000.
7. C) Let the ratio of content = p: q
Quantity of A in the mixture = 5p/6 + 1q/4
Quantity of B in the mixture = 1p/6 + 3q/4
Therefore, the required mixture = 1:1
{5p/6 + 1q/4} / {1p/6 + 3q/4} = 1/1
By solving,
We get p/q = 3/4
8. D) Let the cost price of chair with profit = P
So the cost price of the second chair will be = 545 – P
Because there is no profit no loss in the whole transaction
115P/100 + (545 – P)88/100 = 545
115 P + 47960 – 88 P = 54500
27P = 6540
By solving it for P
The cost price of chair = Rs. 242.222 ≈ Rs.242
9. A) Let the money is invested is 2Y and 3Y
So the total money invested = 5Y
Now money obtained A
A=(2Y x 106/100) + ( 3Y x 91/100)
A= 97Y/20
Now the loss will be
Loss=5Y – 97Y/20
Loss=3Y/20
So the loss percentage will be
[{(3Y/20) / 5Y} x 100]%
Loss % = 3%
10. B) Cash price of the laptop = Rs. 24945
Amount paid by Meera = Rs. 3945
Amount left = Rs. 21000
Now let the value of instalment is P
So the amount paid is
{P/(1+R/100)2} + {P/(1+R/100)1} = 21000
Where P is the value of first installment
And R = 5%
By solving this
{P/(1+5/100)2} + {P/(1+R/100)1}= 21000
P = (21000 x 441)/820
P = 11293.90