Answer

Verified

349.7k+ 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.

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

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

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

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE