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Three women, Isha, Nisha, and Sudha, earn a monthly salary in the ratio 3:4:53:4:5. They also spend monthly in the ratio 3:5:63:5:6, saving the rest. If Sudha's savings are 1/61/6th of her income, what's the ratio of the three women's monthly savings?

Solution

✅ Correct Option: 1

Let their incomes be 3k3k, 4k4k, and 5k5k respectively based on the ratio 3:4:53:4:5.


Sudha's savings are 16\dfrac{1}{6} of her income:

Sudha's savings =16×5k= \dfrac{1}{6} \times 5k

=5k6= \dfrac{5k}{6}

Since Savings = Income - Spending:

Sudha's spending =5k−5k6= 5k - \dfrac{5k}{6}

=30k−5k6= \dfrac{30k - 5k}{6}

=25k6= \dfrac{25k}{6}


From the spending ratio 3:5:63:5:6, if Sudha spends 66 units:

Sudha spends 66 units =25k6= \dfrac{25k}{6}

So 11 unit =25k36= \dfrac{25k}{36}


Isha's spending =3×25k36= 3 \times \dfrac{25k}{36}

=25k12= \dfrac{25k}{12}

Nisha's spending =5×25k36= 5 \times \dfrac{25k}{36}

=125k36= \dfrac{125k}{36}

Sudha's spending =25k6= \dfrac{25k}{6}


Isha's savings =3k−25k12= 3k - \dfrac{25k}{12}

=36k−25k12= \dfrac{36k - 25k}{12}

=11k12= \dfrac{11k}{12}

Nisha's savings =4k−125k36= 4k - \dfrac{125k}{36}

=144k−125k36= \dfrac{144k - 125k}{36}

=19k36= \dfrac{19k}{36}

Sudha's savings =5k6= \dfrac{5k}{6}


Converting to common denominator 3636:

Isha's savings =11k12= \dfrac{11k}{12}

=33k36= \dfrac{33k}{36}

Nisha's savings =19k36= \dfrac{19k}{36}

Sudha's savings =5k6= \dfrac{5k}{6}

=30k36= \dfrac{30k}{36}


Savings ratio =33k36:19k36:30k36= \dfrac{33k}{36} : \dfrac{19k}{36} : \dfrac{30k}{36}

=33:19:30= 33 : 19 : 30

Therefore, the ratio of monthly savings is 33:19:3033 : 19 : 30.

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