Question

The weights of Mr. Gupta and Mrs. Gupta are in the ratio 7: 8 and their combined (total) weight is 120 kg. After taking a dieting course, the weight of Mr. Gupta reduces by 6 kg and the ratio between their weights changes to 5: 6. Find the reduction of weight of Mrs. Gupta due to this dieting course.
A .4
B .5
C .8
D .1

Answer 1

HINT- Proceed the solution of this question, by assuming weights of Mr. Gupta and Mrs. Gupta in terms of their given ratio hence find their initials weights with the help of total weights. Once we get their initial weights then using the weights changes ratio we can find a reduced weight of Mrs. Gupta.

Complete Step-by-Step solution:
In the question it is given that the weights of Mr. Gupta and Mrs. Gupta are in the ratio 7: 8
And we know that
\[{\text{If }}\dfrac{{\text{a}}}{{\text{b}}} = \dfrac{5}{6}\] then with the ratio property we can write a=5k & b=6k
Let the weight of Mr. Gupta be 7a and Mrs. Gupta be 8a.
Their combined weight, 7a+8a=120
⇒15a=120⇒ a=8

Hence, the weight of Mr. Gupta be 7a= 7×8=56kg and Mrs. Gupta be 8a= 8×8=64kg.

Reduced weight of Mr. Gupta =56kg−6kg=50kg
Let the new weight of Mrs. Gupta be 64−b kg where b is the reduction in her weight.

Given, their reduced weights are in the ratio 5:6
⇒50:64−b=5:6
This can be written as
\[ \Rightarrow \dfrac{{50}}{{64 - {\text{b}}}} = \dfrac{5}{6}\]
On cross multiplication
​
⇒300=320−5×b
⇒5×b=20
$ \Rightarrow {\text{b = }}\dfrac{{20}}{5}$
⇒b=4
Hence, Mrs. Gupta’s weight is reduced by 4kg
Hence, option A is correct.

Note- In this particular question we used the concept of ratio and proportion and we have seen how we can use the ratio of various quantities to analyse and compute the different quantities like in the above question we find reduction of weight of Mrs. Gupta.
We should also know that, if ratio of three quantities are given as a:b:c = 1:2:3 then we can also let them a,b,c as =k ,b=2k ,c=3k