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Question 1

A man puts a total of $15000 in the bank in three different schemes I, II and III of investment. The schemes are such that he is returned the same interest after 2, 4 and 8 years from the three schemes respectively. The rate of simple interest for each scheme is 8%. Which of the following statements is true? Indicate all correct statements.

  1. The amounts invested in the three schemes were in ratio 1:2:4
  2. The amounts invested in the three schemes were in ratio 4:2:1
  3. The amounts invested in the three schemes were in ratio 1:1/2:1/4
  4. The ratio of the three investments cannot be determined
  5. The amounts invested in the three schemes cannot be determined

Correct Answer: B and C

Explanation:

Let the three amounts invested in the three schemes I, II and III be a, b and c respectively.
SI = PRT/100 where SI is the simple interest, P, R and T are principle, rate and time.
Since the interest is the same, we get
a*8*2/100 = b*8*4/100 = c*8*8/100
2a=4b=8c
a=2b=4c = k(say)
a=k, b=k/2, c=k/4
a:b:c = 1:1/2:1/4
= 4:2:1
Options B and C are true and A and D are false.
Since we know the ratio in which the total investment of $15000 was divided, we can determine the amounts invested in each scheme.
Option E is false.

Question 2

Which of the following can be a term in the series 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...? Indicate all correct options.

  1. 266
  2. 900
  3. 256
  4. 600
  5. 289

Correct Answer: A

Explanation:

The series contains the squares of natural numbers. Hence, all perfect squares will be elements in the series.
The perfect squares in the given options are 900, 256 and 289
Options B, C and E are correct.

Question 3

In an examination, one mark is given for every correctly answered question and 0.2 marks are deducted for every incorrectly answered question. The number of questions answered correctly by Peter is equal to the number of questions answered wrongly by Ann and vice-versa. If they are not allowed to leave any question unanswered and Ann scores one-third of what Peter does, then which of the following statements is true? Indicate all such statements.

  1. Peter answered half of the questions incorrectly
  2. Peter answered one-third of the questions incorrectly
  3. Ann answered one-fifth of the questions correctly
  4. Ann answered two-third of the questions incorrectly
  5. Ann scored negative marks

Correct Answer: B and D

Explanation:

Let the number of questions answered correctly and incorrectly by Peter be x and y respectively.
Peter's score = x-0.2y
Ann's score = y-0.2x
According to the conditions,
x-0.2y = 3(y-0.2x)
x-0.2y=3y-0.6x
x+0.6x=3y+0.2y
1.6x=3.2y
x=2y
The total number of questions is given by x+y
= 2y+y = 3y
Peter answered y questions incorrectly out of a total of 3y questions.
Hence, Peter answered one-third of the total questions incorrectly.
Option A is false and B is true.

Peter answered 1-1/3=2/3 of the total questions correctly.
Hence, Ann answered two-third of the questions incorrectly.
Option C is false and D is true.
Ann's score = y-0.2x
= y-0.2*2y
= y-0.4y = 0.6y
Since y is positive, 0.6y is positive.
Hence, Ann scored positive marks.
Option E is false.

Question 4

In a race of 600 m, Smith can beat Adam by one-tenth the distance and in a race of 500m, Adam can beat Robert by one-tenth the distance. Which of the following statements is true? Indicate all such statements.

  1. When Smith covers 600 m, Adam covers 560m
  2. When Smith covers 500m, Adam covers 550m
  3. When Adam covers 400m, Robert covers 360m
  4. When Robert covers 500m, Smith covers more than 600m
  5. When Robert covers 500m, Adam covers less than 650m

Correct Answer: C and E

Explanation:

In a race of 600m, Smith covers 600m and Adam covers 600-1/10*600 = 600-60 = 540m
Options A and B are false.

When Adam covers 400m, Robert covers 400-1/10*400 = 400 - 40 = 360m
Option C is true.

Let the distance covered by Smith be x when Robert covers 500m
When Smith covers x meters, Adam covers x-x/10 = 9x/10 m
When Adam covers 9x/10 m, Robert covers 9x/10-1/10*9x/10 = (90-9)x/100 = 81x/100m
When Robert covers 500m, 81x/100=500
x=500*100/81 = 617.28m approximately.
Hence, option D is false and E is true.

Question 5

Two containers contain diluted acid of 0.5 and 0.75 concentration. Which of the following statements is true? Indicate all such statements.

  1. A solution of 2 litres from each container contains acid and water in ratio 1:2
  2. A solution of 2 litres from each container contains acid and water in ratio 5:3
  3. A solution of 3 litres from the first container and 2 litres from the second contains acid and water in ratio 1:2
  4. A solution of 3 litres from each container contains acid and water in ratio 5:3
  5. A solution of 5 litres from each container contains acid and water in ratio 1:2

Correct Answer: B and D

Explanation:

2 litres from the first container contains 2*0.5 = 1 litre of acid and 2-1=1 litres of water
2 litres from the second container contains 2*0.75 = 1.5 litres of acid and 2-1.5=0.5 litres of water
The final solution contains 1+1.5=2.5 litres of acid and 1+0.5=1.5 litres of water
Ratio = 2.5:1.5 = 5:3
Option A is false and B is true.

3 litres from the first container contains 3*0.5 = 1.5 litre of acid and 3-1.5=1.5 litres of water
2 litres from the second container contains 2*0.75 = 1.5 litres of acid and 2-1.5=0.5 litres of water
The final solution contains 1.5+1.5=3 litres of acid and 1.5+0.5=2 litres of water
Ratio = 3:2
Option C is false.

3 litres from the first container contains 3*0.5 = 1.5 litre of acid and 3-1.5=1.5 litres of water
3 litres from the second container contains 3*0.75 = 2.25 litres of acid and 3-2.25=0.75 litres of water
The final solution contains 1.5+2.25=3.75 litres of acid and 1.5+0.75=2.25 litres of water
Ratio = 3.75:2.25 = 5:3
Option D is true.

5 litres from the first container contains 5*0.5 = 2.5 litre of acid and 5-2.5=2.5 litres of water
5 litres from the second container contains 5*0.75 = 3.75 litres of acid and 5-3.75=1.25 litres of water
The final solution contains 3.75+2.25=6.25 litres of acid and 2.5+1.25=3.75 litres of water
Ratio = 6.25:3.75 = 5:3
Option E is false.

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