lcm and hcf Model Questions & Answers, Practice Test for ssc mts paper 1 2023

Question :21

The length and breadth of rectangular field are 55 m and 45 m respectively. The length of the largest rod (in m) that can measure the length and breadth of the field exactly, is

Answer: (a)

So the largest length of rod will be the H.C.F. of length and breadth.

HCF = 5

Length of rod = 5 m.

Question :22

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: (b)

The required number must be a factor of (11284 – 7655) or 3629.

Now, 3629 = 19 × 191

∴ 191 is the required number.

Question :23

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$5/6$ . What is the original fraction?

Answer: (a)

Suppose original fraction is = $x/y$

∵${x+{240/100}x}/{y-{50/100}y}$=$2{5/6}$⇒${x+2.4x}/{y-0.5y}=17/6$

${3.4x}/{0.5y}=17/6$

∴$x/y=17/6$×$0.5/3.4$

$x/y=5/12$

Question :24

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: (a)

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.

Question :25

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

Answer: (a)

The required number = $\text"LCM × HCF"/\text"First number"$ = ${2079 × 27}/189$ = 297

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