# State True or False:

99 Kg : 45 Kg = Rs. 44 : Rs. 20

(a). True

(b). False

Answer

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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.

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.

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