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

Answer & Explanation
Answer : Option
C


Explanation : 







2 . 
If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is $25 \over 51$, what is the original fraction ? 

Answer & Explanation
Answer : Option
C


Explanation : 

${x + 1.5x}\over{y + 3.5y}$ = $25 \over 51$ $2.5x \over 4.5y$ = $25 \over 51$ $x \over y$ = ${25 \times 45}\over{51 \times 25}$ = $15 \over 17$ 





3 . 
When 30% of one number is subtracted from another number, the second number reduces to its fourfifth. What is the ratio between the first and the second number respectively? 

Answer & Explanation
Answer : Option
E


Explanation : 







4 . 
If the numerator of a fraction is increased by 400% and the denominator is increased by 500%. The resultant fraction is $20 \over 27$. What was the original fraction ? 

Answer & Explanation
Answer : Option
E


Explanation : 







5 . 
The difference between the $3 \over 4$th of $4 \over 5$th of a number and $1 \over 6$th of $2 \over 5$th of the same number is 648. What is the number ? 

Answer & Explanation
Answer : Option
B


Explanation : 







6 . 
If 3$4 \over 5$ is subtracted from 6$3 \over 5$ and difference is multiplied by 355 then what will be the final number ? 

Answer & Explanation
Answer : Option
D


Explanation : 







7 . 
If the numerator of a fraction is increased by 240% and the denominator of the fraction is decreased by 50%, the resultant fraction is 2$5 \over 6$. What is the original fraction ? 

Answer & Explanation
Answer : Option
C


Explanation : 







8 . 
If the numerator of a fraction is increased by 200% and the denominator is increased by 300%, the resultant fraction is $15 \over 26$. What was the original fraction ? 

Answer & Explanation
Answer : Option
D


Explanation : 







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 ? 

Answer & Explanation
Answer : Option
C


Explanation : 

The LCM of 18, 22, 30 is 990. So, they will meet each other after 990, ie, 16 min and 30 sec. 





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 ? 

Answer & Explanation
Answer : Option
B


Explanation : 







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. 

Answer & Explanation
Answer : Option
D


Explanation : 

The required number must be a factor of (11284  7655) or 3629. Now, 3629 = 19 $\times$ 191 or 191 is the required number. 





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

Answer & Explanation
Answer : Option
C


Explanation : 

The required number = ${ LCM \times HCF} \over {First \,\,\,number}$ = ${2079 \times 27}\over 189$ = 297 





13 . 
Find the least number which, when divided by 18, 24, 30 and 42, will leave in each case the same remainder 1. 

Answer & Explanation
Answer : Option
A


Explanation : 







14 . 
Find the greatest number of six digits which, no being divided by 6, 7, 8, 9 and 10, leaves 4, 5, 6, 7 and 8 as remainder respectively. 

Answer & Explanation
Answer : Option
A


Explanation : 

The LCM of 6, 7, 8 , 9 and 10 = 2520 The greatest number of 6 digits = 999999 Dividing 999999 by 2520, we get 2079 as remainder.
Hence, the 6digit number divisible by 2520, is (999999  2079), or 997920. Since 6  4 = 2, 7  5 = 2, 8  6 = 2, 9 7 = 2, 10  8 = 2, the remainder in each case is less than the divisor by 2. or the required number = 997920  2 = 997918 





15 . 
what least number must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 will leave in each case the same remainder 7? 

Answer & Explanation
Answer : Option
B


Explanation : 

The LCM of 9, 10 and 15 = 90 On dividing 1936 by 90, the remainder = 46 But 7 is also a part of this remainder. the required number = 46  7 = 39 





16 . 
What greatest number can be subtracted from 10,000 so that the remainder may be divisible by 32, 36, 48 and 54 ? 

Answer & Explanation
Answer : Option
A


Explanation : 

LCM of 32, 36, 48, 54 = 864 the required greatest number = 10,000  864 = 9, 136 





17 . 
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. 

Answer & Explanation
Answer : Option
B


Explanation : 

The least number which, when divided by 8, 12 and 16, leaves 3 as remainder = (LCM of 8, 12, 16) + 3 = 48 + 3 = 51 Other such numbers are 48 $\times$ 2 + 3 = 99, 48 $\times$ 3 + 3 = 147, the required number which is divisible by 7 is 147. 





18 . 
Find the greatest number that will divide 55, 127 and 175 so as to leave the same remainder in each case. 

Answer & Explanation
Answer : Option
B


Explanation : 

Let x be the remainder, then the numbers (55  x), (127  x) and (175  x) are exactly divisible by the required number. Now, we know that if two numbers are divisible by a certain number, then their difference is also divisible by the number. Hence the numbers (127  x)  (55  x), (175  x)  (127  x) and (175  x)  (55  x) or, 72, 48 and 120 are divisible by the required number. HCF of 48, 72 and 120 = 24, therefore the required number = 24. 





19 . 
What least number should be added to 3500 to make it exactly divisible by 42, 49, 56 and 63 

Answer & Explanation
Answer : Option
D


Explanation : 

LCM of 42, 49, 56, 63 = 3528; therefore, the required least number = 3528  3500 = 28 





20 . 
Find the least number which, when divided by 72, 80 and 88, leaves the remainders 52, 60 and 68 respectively. 

Answer & Explanation
Answer : Option
A


Explanation : 

72  52 = 20, 80  60 = 20, 88  68 = 20. We see that in each case, the remainder is less than the divisor by 20. The LCM of 72, 80 and 88 = 7920, therefore, the required number 7920  20 = 7900 





21 . 
Find the greatest number of 4 digits which, when divided by 2, 3, 4, 5, 6 and 7, should leave remainder 1 in each case. 

Answer & Explanation
Answer : Option
A


Explanation : 

The greatest number of 4 digits = 9999. LCM of 2, 3, 4, 5, 6, 7 = 420 On dividing 9999 by 420, we get 339 as remainder. the greatest number of 4 digits which is divisible by 2, 3, 4, 5, 6 and 7 = 9999  339 = 9660 M the required number = 9660 + 1= 9661 





22 . 
The traffic lights at three different road crossings change after every 48 sec., 72 sec., and 108 sec. respectively. If they all change simultaneously at 8:20:00 hrs, then at what time will they again change simultaneously? 

Answer & Explanation
Answer : Option
B


Explanation : 

LCM of 48, 72, 108 = 432 the traffic lights will change simultaneously after 432 seconds or 7 min 12 secs. they will change simultaneously at 8 : 27 : 12 hrs. 





23 . 
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? 

Answer & Explanation
Answer : Option
D


Explanation : 

The first number = 2 $\times$ 44 = 88 The second number = ${HCF \times LCM} \over 88$ = ${44 \times 264} \over 88$ = 132 





24 . 
The product of two number is 2160 and their HCF is 12. Find the possible pairs of numbers 

Answer & Explanation
Answer : Option
B


Explanation : 

HCF = 12. Then let the numbrs be 12x and 12y. Now 12x $\times$ 12y = 2160 xy = 15 Possible values of x and y are (1, 15); (3, 5); (5, 3); (15, 1) the possible pairs of numbers (12, 180) and (36, 60) 





25 . 
Find the greatest number of 4 digits and the least number of 5 digits that have 144 as their HCF. 

Answer & Explanation
Answer : Option
A


Explanation : 

The required numbers should be multiples of 144. We have the greatest number of 4 digits = 9999. On dividing 9999 by 144, we get 63 as the remainder. Required greatest number of 4 digits = 9999  63 = 9936 Again, we have the least number of 5 digits = 10000 On dividing 10,000 by 144, we get 64 as the remainder. the required least number of 5 digits = 10,000 + (144  64) = 10,080 





26 . 
Find the least number that, being increased by 8, is divisible by 32, 36 and 40. 

Answer & Explanation
Answer : Option
A


Explanation : 

LCM of 32, 36 and 40 = 1440, therefore, the required number = 1440  8 = 1432 





27 . 
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? 

Answer & Explanation
Answer : Option
C


Explanation : 

Bells will toll together again at a time, which is obtained by taking L.C.M. of their individual tolling intervals. L.C.M. of 9, 12 and 15 = 180 min They will toll together again after 180 min, i.e. 3 hours. Time = 8 + 3 = 11 a.m. 





28 . 
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? 

Answer & Explanation
Answer : Option
B


Explanation : 







29 . 
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? 

Answer & Explanation
Answer : Option
A


Explanation : 







