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Arithmetic : Level 2 Test - 1
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Question 1 |
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?
4 min | |
7 min | |
6 min | |
None of these |
Question 1 Explanation:
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 = 44 /9
Hence answer is none of these i.e option D.
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 = 44 /9
Hence answer is none of these i.e option D.
Question 2 |
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?
Rs. 16000 | |
Rs. 15000 | |
Rs. 15600 | |
Rs. 14600 |
Question 2 Explanation:
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
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
Question 3 |
A man divided his share between his sons A and B in such a way that the interest received by A at 15% per annum for 3 yr is double the interest received by B at 12% per annum for 5 yr. It what ratio was hisshare divided?
2/3 | |
8/3 | |
3/8 | |
3/2 |
Question 3 Explanation:
Let the share of a A = Rs p
Let the share of a B = Rs q
Therefore from the question, the equation for simple interest received by the two sons is as follows:
(p x 15 x 3) / 100 = 2 x (q x 15 x 3) / 100
p/q = (2 x 12 x 5 )/ 15 x 3 = 8/3
Let the share of a B = Rs q
Therefore from the question, the equation for simple interest received by the two sons is as follows:
(p x 15 x 3) / 100 = 2 x (q x 15 x 3) / 100
p/q = (2 x 12 x 5 )/ 15 x 3 = 8/3
Question 4 |
Ms Sharma's expenditure and savings are in the ratio of 3: 2. Her income increases by 10%. Her expenditure also increases by 12%. By what percentage do her savings increase?
7% | |
6% | |
13% | |
11% |
Question 4 Explanation:
Let Ms. Sharma’s saving = 2s
Let Ms. Sharma’s expenditure = 3s
Therefore, his initial total income becomes 5s
Now her income increases by 10 % so
New income will be 5.5s
Her expenditure increases by 12 % and therefore
Her new expenditure 3s x 12% = 3.36s
Therefore, her new saving is 5.5s – 3.36s = 2.14s
Percentage Increase in savings = (2.14s – 2s)/2s x 100 = 7%
Let Ms. Sharma’s expenditure = 3s
Therefore, his initial total income becomes 5s
Now her income increases by 10 % so
New income will be 5.5s
Her expenditure increases by 12 % and therefore
Her new expenditure 3s x 12% = 3.36s
Therefore, her new saving is 5.5s – 3.36s = 2.14s
Percentage Increase in savings = (2.14s – 2s)/2s x 100 = 7%
Question 5 |
The ratio of milk to water in three containers of equal capacity is 3 : 2, 7 : 3 and 11 : 4 respectively. The three containers are mixed together. What is the ratio of milk to water after mixing?
38 : 8 | |
21: 9 | |
61: 29 | |
41: 18 |
Question 5 Explanation:
To do these types first let the value of the total mixture
Let it be 30 l
We take 30 l for simple calculations and 30 is the common factor of 5, 10, 15
Now therefore the Quantity of Milk after mixing will be (3/5 + 7/10 + 11/15) x 30 = 61 l
Now the Quantity of water after mixing will be
(2/5 + 3/10 + 4/15) x 30 = 29 l
Therefore the required ratio will be = 61 : 29
We take 30 l for simple calculations and 30 is the common factor of 5, 10, 15
Now therefore the Quantity of Milk after mixing will be (3/5 + 7/10 + 11/15) x 30 = 61 l
Now the Quantity of water after mixing will be
(2/5 + 3/10 + 4/15) x 30 = 29 l
Therefore the required ratio will be = 61 : 29
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