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- The ratio of boys to girls in a class of 70 students is 4 : 3. Among the girls the ratio of sports person to non-sports person is 1 : 4. And the ratio of sports person to non-sports person in the class is 8 : 27. Find the ratio of the sports person to non-sports person among boys in the class.
A) 2 : 7
B) 1 : 3
C) 2 : 5
D) 1 : 4
E) 3 : 5B) 1 : 3
Explanation:
Boys in class = (4/7)*70 = 40, so girls = 70-40=30
Among girls, spots persons = (1/5)*30 = 6, so non-sports persons = 30-6 = 24
Total sports person in class = 8/(8+27) * 70 = 16, so non-sports persons = 70-16 = 54
So among boys sports person = 16-6=10, non-sports = 54-24 = 30
So ratio = 10: 30 = 1: 3 - In a group of 11 people, the average age of the oldest and the youngest is 11 years. If anyone these of these persons leave the group, the maximum and minimum average of remaining is 12 years and 11 years respectively. Find the average age of the entire group.
A) 11 5/11 years
B) 12 years
C) 11 7/11 years
D) 10 years
E) 9 ½ yearsA) 11 5/11 years
Explanation:
Let total age of 9 people except oldest and youngest = a years
Age of oldest = x years, age of youngest = y yeas
Then (x+y)/2 = 11, gives x + y = 22
Then (a+x)/10 = 11, gives a + x = 110
Then (a+y)/10 = 12, gives a + y = 120
Now there are 3 equations, solve and find all values, a = 104, x = 16, y = 6
Then average = (104+16+6)/11 - A and B invest Rs 24,000 and Rs 36,000 respectively in a business. They have an agreement that half of the total profit will be divided equally between them, and remaining half profit will be divided between then in the ratio of their investments. If they would have shared the entire profit in the ratio of their capitals, B would have got Rs 2500 more than what he would have got otherwise. What is the total profit?
A) Rs 48,000
B) Rs 50,000
C) Rs 51,000
D) Rs 51,500
E) Rs 50,500B) Rs 50,000
Explanation:
24000 : 36000
2 : 3
Let total profit = Rs x
Then B would have got = [3/(2+3)] *x = 3x/5
If they divide half of profit between then equally, B will get (x/2)/2 = x/4, then from remaining x/2, B will get [3/(2+3)] *(x/2) = 3x/10
Now –
3x/5 = x/4 + 3x/10 + 2500
Solve, x = 50,000 - Alloy A is made up of copper and zinc. It has 42 6/7% copper. If 6 gms of copper is added to it, it would have 60% copper. Find the initial weight of A(in gms).
A) 15.5
B) 21
C) 10.5
D) 14
E) 17.5D) 14
Explanation:
42 6/7 = 300/7%
Then
(300/7*100) * x + 6 = (60/100) * (x+6)
Solve, x = 14 - 2/5th of work is done in 8 days by 10 people working 5 hours each day. If the remaining work is to be completed in a total of 14 days working same number of hours each day as earlier, how many additional men are needed to complete the work?
A) 11
B) 10
C) 20
D) 18
E) 12B) 10
Explanation:
Total work to be completed in 14 days, so (additional men+10 men already employed) will have to complete remaining work (1 – 2/5 ) = 3/5 of work in (14-8) = 6 days.. let x is additional men
M1*D1*H1*W2 = M2*D2*H2*W1
10*8*5*(3/5) = (10+x)*6*5*(2/5)
Solve x = 10 - What is the cost price of the cycle?
I. The cost price is 10 times the profit, and the selling price is Rs 165.
II. The profit is 10% of Rs 150, the selling price.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
Explanation:
From I: CP = 10P, SP = 165, P = SP – CP = 165 – 10P, so 11P = 165, P = Rs 15
CP = 150
From II: CP = (100/110)*150 - Pipes A, B and C can be used for filling or emptying. If A and B are used for filling and C for emptying, tank would be filled in 6 hours. Find the time taken by C to fill the tank.
I. If all pipes used for filled tank will be filled in 2 hours.
II. If B and C are used for filling and A used for emptying, tank would be filled in 6 hours.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.A) If the data in statement I alone is sufficient to answer the question.
Explanation:
From I: (1/A + 1/B + 1/C) = 1/2
And given 1/A + 1/B – 1/C = 1/6
Subtract both equations and find C
From II: 1/B + 1/C – 1/A = 1/6
And given 1/A + 1/B – 1/C = 1/6
From these equations, C cannot be find out. - What is the rate of interest on a certain sum of money?
I. A total of Rs 3000 is obtained as the CI on sum of money at the end of 3 years.
II. At same rate, the difference between SI and CI obtained at the end of 2 years is Rs 80.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.(E) If the data in both the statements I and II together are necessary to answer the question.
Explanation:
From I: 3000 = P [(1 + r/100)2 – 1]
From II: Pr2/1002 = 80
From I and II we have 2 equations in 2 variables which can be solved to find P. - What is the difference between the present ages of A and B?
I. One sixth of A’s age is equal to one fourth of B’s age.
II. The ages of A and B is in the ratio is 5 : 3
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.(D) If the data given in both I and II together are not sufficient to answer the question.
Explanation:
From I: A’ age = 5x, B’s age = 3x
From II: (1/6) * 3x = (1/4) * 2x. This gives 1/2 = 1/2
We do not get anything from any statement. - In how much time will A reach his destination?
I. The speeds of A and B is in the ratio 3 : 2
II. B took 45 minutes to reach the destination.
A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.(E) If the data in both the statements I and II together are necessary to answer the question.
Explanation:
From I: speeds of A and B are 3x and 2x respectively.
From II: B’s time = 45 minutes
Since distance is same, from both statements:
So 2x*45 = 3x* A’s time
So A’s time = 30 minutes.
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