Question

The length of the ribbon was originally 30 cm. It was reduced in the ratio 5:3. What is its length now?
(a) 15
(b) 18
(c) 20
(d) 25

Answer 1

Hint: First of all, let the reduced length of the ribbon be x. Now use, \[\dfrac{\text{Original Length}}{\text{Reduced Length}}=\dfrac{5}{3}\]. Substitute the value of the original length of the ribbon and then cross multiply and simplify the equation and get the reduced length of the ribbon.

Complete step-by-step answer:
In this question, we are given that the length of the ribbon was originally 30 cm. It was reduced in the ratio 5:3. We have to find the reduced length of the ribbon. Let us assume the new length or the reduced length of the ribbon as x cm.
Let us find the ratio of the original length of the ribbon to the reduced length of the ribbon. So, we get,
\[\text{Ratio of the original length to the reduced length}=\dfrac{\text{Original length of the Ribbon}}{\text{Reduced length of the Ribbon}}\]
By substituting the value of the original length as 30 cm and reduced length as x in the above equation, we get,
\[\text{Ratio of the original length to the reduced length}=\dfrac{30}{x}.....\left( i \right)\]
We are given that the length is reduced in the ratio 5:3. So, we get,
\[\text{Ratio of the original length to the reduced length}=5:3=\dfrac{5}{3}....\left( ii \right)\]
By equating the value of the ratio of the original length to the reduced length from equation (i) and (ii), we get,
\[\dfrac{30}{x}=\dfrac{5}{3}....\left( iii \right)\]
By cross multiplying the above equation, we get,
\[30\times 3=5x\]
By dividing 5 on both the sides of the above equation, we get,
\[\dfrac{30\left( 3 \right)}{5}=x\]
\[x=6\times 3\]
x = 18 cm.
So, we get the reduced length of the ribbon as 18 cm.
Hence, option (b) is the right answer.

Note: In this question, many students make this mistake of multiplying \[\dfrac{5}{3}\] by the original length that is 30 cm which is wrong because we are clearly given that the length is reduced but if we multiply 30 by \[\dfrac{5}{3}\] that is \[30\times \dfrac{5}{3}\], we get 50 cm which is more than 30 cm. Also, students must note that if we have an equation \[\dfrac{a}{b}=\dfrac{c}{d}\] and here a > b implies c > d and vice versa. Similarly, b > a implies d > c and vice versa. In this question, students can cross-check their answer by substituting x = 18 cm in equation (iii) and checking if LHS = RHS or not.