The HCF and LCM of two numbers are 22 and 2400 respectively. If one number is 264 then find another number?
100
150
200
250
Answer: (c) 200Solution: Given, HCF = 22LCM = 2400First number = 264Let the second number is \(x\) then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ 264 \times x = 22 \times 2400 $$ $$ x = \frac{22 \times 2400}{264} $$ $$ x = \frac{52800}{264} $$ $$ x = 200 $$ Hence the second number is 200.
Find the smallest sum of rupees which contains Rs 1.25, Rs 15, Rs 2.50, and Rs 10?
30
35
40
45
Answer: (a) 30Solution: Given, Rs 1.25, Rs 15, Rs 2.50, and Rs 10 thenLCM of 1.25, 15, 2.50, and 10It can be also written\((LCM \ of \ 125, 1500, 250, 1000) \times 0.01\) $$ = 3000 \times 0.01 $$ $$ = 30 $$ Hence Rs 30 is the smallest sum of rupees.
Three women start walking together to the same way around a circular track of 15 km. If their speeds are 3, 4, and 5 km per hour respectively then find how much time they will take to meet together again?
10 hours
12 hours
15 hours
18 hours
Answer: (c) 15 hoursSolution: Time taken by the women to complete one revolution of the circular way $$ = \frac{15}{3}, \frac{15}{4}, \ and \ \frac{15}{5} \ hours $$ $$ = \frac{5}{1}, \frac{15}{4}, \ and \ \frac{3}{1} \ hours $$ Taking LCM of \(\frac{5}{1}, \frac{15}{4}, \ and \ \frac{3}{1}\) $$ = \frac{LCM \ of \ 5, 15, 3}{HCF \ of \ 1, 4, 1} $$ $$ = \frac{15}{1} $$ $$ 15 \ hours $$ Hence the women will meet together again after 15 hours.
The LCM and HCF of two numbers are 1350 and 25 respectively. If one number is 125 then find another number?
200
270
290
300
Answer: (b) 270Solution: Given, LCM = 1350HCF = 25First number = 125Let the second number is \(x\) then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ 125 \times x = 25 \times 1350 $$ $$ x = \frac{25 \times 1350}{125} $$ $$ x = \frac{33750}{125} $$ $$ x = 270 $$ Hence the second number is 270.
If HCF of 575 and 325 is 65 then find the LCM of the same numbers?
2525
2775
2825
2875
Answer: (d) 2875Solution: Given, first number = 575second number = 325HCF = 65 then $$ Product \ of \ two \ numbers = HCF \times LCM $$ $$ LCM = \frac{Product \ of \ two \ numbers}{HCF} $$ $$ LCM = \frac{575 \times 325}{65} $$ $$ LCM = \frac{186,875}{65} $$ $$ LCM = 2875 $$