Question

Four bells commence tolling together. They toll at intervals of 2,2¼, 4½ and 2¾ second respectively. After what time will they toll together again.

Answer 1

Step-by-step explanation:

see the picture given above it gives the perfect answer

Answer 2

Answer:

The bells toll together after 198 seconds.

Step-by-step explanation:

Given,

Four bells commence tolling together and the interval at which they toll respectively are 2,2¼, 4½, and 2¾ seconds

To find,

The time duration in which the four bells toll together

Recall the concept

LCM of fractions = $\frac{LCM \ of \ numerators}{HCF\ of \ denominators}$ ---------(1)

Solution

The duration in which the four bells toll together is = LCM (2,2¼, 4½, 2¾)

= LCM ( 2, $\frac{9}{4},\frac{9}{2} ,\frac{11}{4}$)

Here, The numerators are 2,9,9,11

LCM of the numerators = 2×9×11 = 198

The denominators are 1,4,2,4

The HCF of the denominators = 1

LCM ( 2, $\frac{9}{4},\frac{9}{2} ,\frac{11}{4}$) = = $\frac{LCM \ of \ numerators}{HCF\ of \ denominators}$ = $\frac{198}{1}$ = 198seconds

The time duration between the bells toll together 198seconds

∴ The bells toll together after 198 seconds.

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