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Q.

State true or false.

In a bag, there are 20 kg of fruits. If $7 \frac{1}{6} kg$ of these fruits are oranges and $8 \frac{2}{3} kg$ of these are apples and the rest are grapes. Then, the mass of the grapes in the bag would be $\frac{41}{6}$ kg.

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a

True

b

False

answer is A.

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Detailed Solution

The above given statement is true.
Concept- This is a fairly straightforward question; first, find the entire mass of the oranges and apples, and then subtract that total mass from the acquired total.
Since there are three different types of fruits, the individual masses of each of the three fruits added together must match the stated total mass of the fruits, which is 20 kg.
Total fruit mass equals the mass of oranges, apples, and grapes.
We can easily observe that the masses are supplied in mixed fractions in this instance. However, we must turn them into an improper fraction in order to perform algebraic operations like addition and subtraction.
Fruits weigh a total of =20kg (1)
Oranges weigh

\frac{71}{6} kg .

Incorrect fraction:

\frac{43}{6}

Thus, the mass of oranges is kg (2)
Apples have a mass of

= 8 \frac{2}{3} kg = (8 \times 3 + \frac{2}{3}) = \frac{26}{3} kg \dots

.(3)
Let the grape mass be x kg (4)
Changing the values in equations (1), (2), (3), and (4)

\frac{43}{6} + \frac{26}{3} + x = 20

x = \frac{41}{6}

So, the given statement is right.
Hence, the correct answer is option 1.

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