Question

Verify the following 60: 105: 84: 147

Answer 1

Given:

Verify the following 60: 105 : : 84: 147

Solution:

60: 105 : : 84 : 147

$= > \dfrac{60}{105} = \dfrac{60 \div 15}{105 \div 15} = \dfrac{4}{7}$

$= > \dfrac{84}{147} = \dfrac{80 \div 21}{147 \div 21} = \dfrac{4}{7}$

Given Ratios are in direct proportion to each other.

Another way to verify:

60 and 147 are Extreme terms.

105 and 84 are middle terms

The product of Extreme Terms is equal to the product of middle terms.

=> Extreme Terms = 60 x 147 = 8820

=> Middle Terms = 105 x 84 = 8820.

Hence, Verified.

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Answer 2

Given data:

60 : 105 : :  84 : 147

To verify:

The relation between them.

Solution:

60 : 105 : :  84 : 147   ⇒   $\frac{60}{105} : \frac{84}{147}$

Lcm of 60 and 105 is 15, and for 84 and 147 is 21.

So, by dividing both the numerator and denominator on the left side with 15, and on right side with 21, we get:

                                 ⇒  $\frac{60/15}{105/15} : \frac{84/21}{147/21}$

                                 ⇒ $\\\frac{4}{7} : \frac{4}{7}$

Here, a/b = c/d i.e., a:b = c:d.

So, the given statement 60: 105:: 84: 147 is in direct proportion.

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