State True or False:
99 Kg : 45 Kg = Rs. 44 : Rs. 20
(a). True
(b). False
Answer
279.5k+ views
Hint: Convert the given equation into the numerator and denominator form. Then solve both the left hand side and the right hand side of the equation and see the result. If they become equal then the equation is true or else it is false.
Complete step-by-step solution -
To state whether the equation is true or false we have to write it down and solve it as follows,
99 Kg : 45 Kg = Rs. 44 : Rs. 20
In the above equation we have given the ratio of mass on the left hand side of the equation and their rates ratio on the right hand side of the equation.
As they have given us the ratios on the both sides therefore the equation will be true only if the ratios of both the sides become equal.
Therefore we have to solve the each side of the equation to check the equality,
Consider,
L.H.S. (Left Hand Side) = 99 Kg : 45 Kg
Above equation can also be written as,
Therefore, L.H.S. (Left Hand Side) $=\dfrac{99Kg.}{45Kg.}$
As both numerator and denominator have same units therefore we can cancel the units, therefore we will get,
Therefore, L.H.S. (Left Hand Side) $=\dfrac{99}{45}$
If we divide both the numerator and denominator by ‘9’ we will get,
Therefore, L.H.S. (Left Hand Side) $=\dfrac{\dfrac{99}{9}}{\dfrac{45}{9}}$
Therefore, L.H.S. (Left Hand Side) $=\dfrac{11}{5}$ …………………………………………….. (1)
Also consider,
R.H.S. (Right Hand Side) = Rs. 44 : Rs. 20
Above equation can also be written as,
Therefore, R.H.S. (Right Hand Side) $=\dfrac{Rs.44}{Rs.20}$
As both numerator and denominator have same units therefore we can cancel them,
Therefore, R.H.S. (Right Hand Side) $=\dfrac{44}{20}$
If we divide both numerator and denominator by ‘4’ we will get,
Therefore, R.H.S. (Right Hand Side) $=\dfrac{\dfrac{44}{4}}{\dfrac{20}{4}}$
Therefore, R.H.S. (Right Hand Side) $=\dfrac{11}{5}$ ………………………………………………….. (2)
L.H.S. (Left Hand Side) = R.H.S. (Right Hand Side)
Therefore we can write,
99 Kg : 45 Kg = Rs. 44 : Rs. 20
Therefore we can say that the given equation is True.
Therefore the correct answer in option (a)
Note: Students generally get confused as there is no extra information and they leave the problem by assuming it’s a wrong problem. But always represent this problem into numerator and denominator form and then solve it.
Complete step-by-step solution -
To state whether the equation is true or false we have to write it down and solve it as follows,
99 Kg : 45 Kg = Rs. 44 : Rs. 20
In the above equation we have given the ratio of mass on the left hand side of the equation and their rates ratio on the right hand side of the equation.
As they have given us the ratios on the both sides therefore the equation will be true only if the ratios of both the sides become equal.
Therefore we have to solve the each side of the equation to check the equality,
Consider,
L.H.S. (Left Hand Side) = 99 Kg : 45 Kg
Above equation can also be written as,
Therefore, L.H.S. (Left Hand Side) $=\dfrac{99Kg.}{45Kg.}$
As both numerator and denominator have same units therefore we can cancel the units, therefore we will get,
Therefore, L.H.S. (Left Hand Side) $=\dfrac{99}{45}$
If we divide both the numerator and denominator by ‘9’ we will get,
Therefore, L.H.S. (Left Hand Side) $=\dfrac{\dfrac{99}{9}}{\dfrac{45}{9}}$
Therefore, L.H.S. (Left Hand Side) $=\dfrac{11}{5}$ …………………………………………….. (1)
Also consider,
R.H.S. (Right Hand Side) = Rs. 44 : Rs. 20
Above equation can also be written as,
Therefore, R.H.S. (Right Hand Side) $=\dfrac{Rs.44}{Rs.20}$
As both numerator and denominator have same units therefore we can cancel them,
Therefore, R.H.S. (Right Hand Side) $=\dfrac{44}{20}$
If we divide both numerator and denominator by ‘4’ we will get,
Therefore, R.H.S. (Right Hand Side) $=\dfrac{\dfrac{44}{4}}{\dfrac{20}{4}}$
Therefore, R.H.S. (Right Hand Side) $=\dfrac{11}{5}$ ………………………………………………….. (2)
L.H.S. (Left Hand Side) = R.H.S. (Right Hand Side)
Therefore we can write,
99 Kg : 45 Kg = Rs. 44 : Rs. 20
Therefore we can say that the given equation is True.
Therefore the correct answer in option (a)
Note: Students generally get confused as there is no extra information and they leave the problem by assuming it’s a wrong problem. But always represent this problem into numerator and denominator form and then solve it.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
State Gay Lusaaccs law of gaseous volume class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

What is pollution? How many types of pollution? Define it

Change the following sentences into negative and interrogative class 10 english CBSE

Which is the tallest animal on the earth A Giraffes class 9 social science CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
