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Three women Swati, Khyati and Tripti earn a monthly salary in the ratio 3:4:5. They also invest part of this salary regularly each month, in the ratio 3:5:6, spending the rest. If Tripti spends a monthly amount that is 3/4th3/4^{th} of her income, what's the ratio of the three women's monthly spending, in the same order as mentioned above?

Solution

✅ Correct Option: 2

Let the monthly salaries of Swati, Khyati, and Tripti be 3k,4k,5k3k, 4k, 5k respectively.

Let their monthly investments be 3m,5m,6m3m, 5m, 6m respectively.


Tripti spends 34\frac{3}{4} of her income, so she invests the remaining 14\frac{1}{4}:

6m=14×5k6m = \frac{1}{4} \times 5k

6m=5k46m = \frac{5k}{4}

m=5k24m = \frac{5k}{24}


Now, expressing each person's investment in terms of kk:

Swati's investment =3m=3×5k24=15k24= 3m = 3 \times \frac{5k}{24} = \frac{15k}{24}

Khyati's investment =5m=5×5k24=25k24= 5m = 5 \times \frac{5k}{24} = \frac{25k}{24}

Tripti's investment =6m=6×5k24=30k24= 6m = 6 \times \frac{5k}{24} = \frac{30k}{24}


Spending == Salary −- Investment

Swati's spending =3k−15k24=72k−15k24=57k24= 3k - \frac{15k}{24} = \frac{72k - 15k}{24} = \frac{57k}{24}

Khyati's spending =4k−25k24=96k−25k24=71k24= 4k - \frac{25k}{24} = \frac{96k - 25k}{24} = \frac{71k}{24}

Tripti's spending =5k−30k24=120k−30k24=90k24= 5k - \frac{30k}{24} = \frac{120k - 30k}{24} = \frac{90k}{24}


Ratio of monthly spending =57k24:71k24:90k24= \frac{57k}{24} : \frac{71k}{24} : \frac{90k}{24}

=57:71:90= 57 : 71 : 90

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