Question

Divide 35 Sweets between and
tanish is the ratio 1/2:1/3​

Answer 1

➤ Correct Question :-

Divide 35 sweets between Rajat and Tanish in the ratio of ½:⅓.

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★ How to do :-

Here, we are given with the total number of sweets that should be divided between two people Rajat and Tanish. We are given with the ratio of division between them. The ratio given to us is ½:⅓. The first part of the ratio represents the parts to be given to Rajat and the second part of the ratio represents the parts given to Tanish. To find the answer, we use two other concepts such as the variables and the transposition method. In the first method, we represent the parts to be givenq to each of them by a variable and find the value of that variable by transposition method. In this method, we shift the numbers or variables from one hand side to the other. This process changes the sign of the appropriate variable or numbers. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \dfrac{1}{2} : \dfrac{1}{3} = 35}$

Take a variables to both part of ratios and add both of them.

${\sf \leadsto \dfrac{1}{2} x + \dfrac{1}{3} x = 35}$

LCM of 2 and 3 is 6.

${\sf \leadsto \dfrac{1 \times 3}{2 \times 3} x + \dfrac{1 \times 2}{3 \times 2} x = 35}$

Multiply the numerators and denominators of both fractions.

${\sf \leadsto \dfrac{3}{6} x + \dfrac{2}{6} x = 35}$

Write both numerators with a common denominator.

${\sf \leadsto \dfrac{3 + 2}{6} x = 35}$

Add the numerators in LHS.

${\sf \leadsto \dfrac{5}{6} x = 35}$

Shift the fraction on LHS to RHS, changing it's sign.

${\sf \leadsto x = 35 \div \dfrac{5}{6}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto x = \dfrac{35}{1} \times \dfrac{6}{5}}$

Write both numerators and denominators with a common fraction.

${\sf \leadsto x = \dfrac{35 \times 6}{1 \times 5}}$

Multiply the numerators and denominators on RHS.

${\sf \leadsto x = \dfrac{210}{5}}$

Simplify the fraction to get the value of x.

${\sf \leadsto x = 42}$

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Now, multiply the value of x with both the part of ratio.

Part of Rajat :-

${\sf \leadsto \dfrac{1}{2} x = \dfrac{1}{2} \times 42}$

Multiply the numbers to get the parts of Rajat.

${\sf \leadsto \dfrac{42}{2} = 21 \: sweets}$

Parts of Tanish :-

${\sf \leadsto \dfrac{1}{3} x = \dfrac{1}{3} \times 42}$

Multiply the numbers to get the parts of Tanish.

${\sf \leadsto \dfrac{42}{3} = 14 \: sweets}$

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${\red{\underline{\boxed{\bf So, \: Rajat \: and \: Tanish \: gets \: 21 \: and \: 14 \: sweets \: respectively.}}}}$