Question

A rope is to be measured an exact number of times by three different measuring tapes of

length 1m 20cm, 70cm and 1m.

I) Find the smallest length of the rope

A) 40m B). 420cm C). 42m D) None of these

ii) Find the number of times it can be measured by the 1st tape

A) 30 B). 35 C). 42 D) 60

iii) Find the number of times it can be measured by the 2nd tape

A) 60 B). 50 C). 40 D) 42

iv) Find the number of times it can be measured by the 3rd tape if length of the tape is doubled

A) 80 B). 70 C). 84 D) None of these​


pls give the answer with the pic of the working ​

Answer 1

Answer i) :-

Prime factors of 120 cm , 70 cm and 100 cm.

→ 120 = 2 * 2 * 2 * 3 * 5

→ 70 = 2 * 5 * 7

→ 100 = 2 * 2 * 5 * 5

so,

→ LCM = 8 * 3 * 5 * 5 * 7 = 4200 cm = 42 m. (C) (Ans.)

then,

→ The number of times it can be measured by the 1st tape = 4200/120 = 35 (B)

and,

→ The number of times it can be measured by the 2nd tape = 4200/70 = 60 (A)

also,

→ The number of times it can be measured by the third tape when length of tape is doubled = (4200*2)/100 = 84 (C)

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