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LCM, HCF and Fraction

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Q 1. The respective ratio between the present ages of Ram and Rakesh is {tex} 6: 11 . {/tex} Four years ago, the ratio of the ages was 1: 2 respectively. What will be Rakesh's age after five years?

45 years

29 years

49 years

Cannot be determined

None of these

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Q 2. If the numerator of a fraction is increased by {tex} 150 \% {/tex} and the denominator of the fraction is increased by {tex} 350 \% , {/tex} the resultant fraction is {tex} \frac { 25 } { 51 } , {/tex} what is the original fraction?

{tex} \frac { 11 } { 17 } {/tex}

{tex} \frac { 11 } { 15 } {/tex}

{tex} \frac { 15 } { 17 } {/tex}

{tex} \frac { 13 } { 15 } {/tex}

None of these

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Q 3. When {tex} 30 \% {/tex} of one number is subtracted from another number, the second number reduces to its four-fifth. What is the ratio between the first and the second number respectively?

4: 7

3: 2

2: 3

Cannot be determined

None of these

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Q 4. If the numerator of a fraction is increased by {tex} 400 \% {/tex} and the denominator is increased by {tex} 500 \% . {/tex} The resultant fraction is {tex} \frac { 20 } { 27 } . {/tex} What was the original fraction?

{tex} \frac { 9 } { 8 } {/tex}

{tex} \frac { 11 } { 12 } {/tex}

{tex} \frac { 8 } { 9 } {/tex}

Cannot be determined

None of these

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Q 5. The difference between the {tex} \frac { 3 } { 4 } {/tex}th of {tex} \frac { 4 } { 5 } {/tex}th of a number and {tex} \frac { 1 } { 6 } {/tex}th of {tex} \frac { 2 } { 5 } {/tex}th of the same number is {tex} 648 . {/tex} What is the number?

1110

1215

1325

1440

None of these

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Q 6. If {tex} 3 \frac { 4 } { 5 } {/tex} is subtracted from {tex} 6 \frac { 3 } { 5 } {/tex} and difference is multiplied by 355 then what will be the final number?

1004

884

774

994

None of these

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Q 7. If the numerator of a fraction is increased by {tex} 240 \% {/tex} and the denominator of the fraction is decreased by {tex} 50 \% , {/tex} the resultant fraction is {tex} 2 \frac { 5 } { 6 } . {/tex} What is the original fraction?

{tex} \frac { 1 } { 4 } {/tex}

{tex} \frac { 2 } { 3 } {/tex}

{tex} \frac { 5 } { 12 } {/tex}

{tex} \frac { 4 } { 11 } {/tex}

None of these

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Q 8. If the numerator of a fraction is increased by {tex} 200 \% {/tex} and the denominator is increased by {tex} 300 \% , {/tex} the resultant fraction is {tex} \frac { 15 } { 26 } . {/tex} What was the original fraction?

{tex} \frac { 8 } { 11 } {/tex}

{tex} \frac { 10 } { 11 } {/tex}

{tex} \frac { 9 } { 13 } {/tex}

{tex} \frac { 10 } { 13 } {/tex}

None of these

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Q 9. Philip, Tom and Brad start jogging around a circular field and complete a single round in 18, 22 and 30 seconds respectively, In how much time, will they meet again at the starting point ?

3 min 15 sec

21 min

16 min 30 sec

12 min

None of these

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Q 10. Amit, Sucheta and Neeti start running around a circular track and complete one round in 18, 24 and 32 seconds respectively. In how many seconds will the three meet again at the starting point if they all have started running at the same time ?

196

288

324

Cannot be determined

None of these

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Q 11. The numbers 11284 and 7655, when divided by a certain number of three digits, leave the same remainder. Find that number of three digits.

161

171

181

191

None of these

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Q 12. The LCM of two numbers is 2079 and their HCF is 27. If one of the numbers is189, find the other.

273

279

297

307

None of these

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Q 13. Find the greatest number of six digits which, on being divided by 6, 7, 8, 9 and 10, leaves 4, 5, 6, 7 and 8 as remainder respectively.

997918

997919

997914

997916

None of these

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Q 14. Find the least number which, when divided by 8, 12 and 16, leaves 3 as the remainder in each case; by 7 leaves no remainder.

145

147

148

157

None of these

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Q 15. Find the greatest number that will divide 55, 127 and 175 so as to leave the same remainder in each case.

26

24

23

29

None of these

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Q 16. What least number should be added to 3500 to make it exactly divisible by 42, 49, 56 and 63?

10

18

25

28

None of these

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Q 17. Find the least number which, when divided by 72, 80 and 88, leaves the remainders 52, 60 and 68 respectively.

7900

7800

7200

7600

None of these

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Q 18. The HCF and LCM of two numbers are 44 and 264 respectively. If the first number is devided by 2, the quotient is 44. What is the other number?

108

44

124

132

None of these

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Q 19. The product of two number is 2160 and their HCF is 12. Find the possible pairs of numbers.

1

2

3

4

None of these

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Q 20. Find the least number that, being increased by 8, is divisible by 32, 36 and 40.

1432

1492

1472

1570

None of these

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Q 21. Three bells toll at intervals of 9, 12 and 15 minutes respectively. All the three begin to toll at 8 a.m. At what time will they toll together again?

8.45 a.m.

10. 30 a.m.

11.00 a.m.

1. 30 p.m.

None of these

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Q 22. Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?

27

36

43

400

402

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Q 23. In a morning walk, three persons step off together, their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that they can cover the distance in complete steps?

122 m 40 cm

123 m 45 cm

122 m 45 cm

122 m 50 cm

None of these

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Q 24. HCF of 3240, 3600 and a third number is 36 and their LCM is {tex} 2 ^ { 4 } \times 3 ^ { 5 } \times 5 ^ { 2 } \times 7 ^ { 2 } {/tex}. The third number is:

{tex} 2 ^ { 4 } \times 5 ^ { 3 } \times 7 ^ { 2 } {/tex}

{tex} 2 ^ { 2 } \times 3 ^ { 5 } \times 7 ^ { 2 } {/tex}

{tex} 2 ^ { 3 } \times 3 ^ { 5 } \times 7 ^ { 2 } {/tex}

{tex} 2 ^ { 5 } \times 5 ^ { 2 } \times 7 ^ { 2 } {/tex}

None of these

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