Sandeep spends 32% of his annual income on food, 20% of the remaining income on travelling, and 35% of the remaining income on clothes, and still saves ₹70,720 per year. What is the annual income (in ₹) of Sandeep?
- A4,50,000
- B5,44,000
- C2,00,000
- D3,75,000
Solution & Step-by-step Explanation
Let Sandeep's annual income be I.
Spending on food = 32% of I
Remaining income after food:
100%−32%=68% of I=0.68I
Spending on travelling = 20% of the remaining income
Remaining income after travelling:
(100%−20%) of 0.68I=80% of 0.68I=0.80×0.68I
Spending on clothes = 35% of the remaining income
Final remaining savings:
(100%−35%) of (0.80×0.68I)=65% of (0.80×0.68I)=0.65×0.80×0.68I
Given that the savings are ₹70,720:
0.65×0.80×0.68×I=70720
100
65
×
100
80
×
100
68
×I=70720
20
13
×
5
4
×
25
17
×I=70720
20×5×25
13×4×17
×I=70720
2500
884
×I=70720
I=
884
70720×2500
Dividing 70720 by 884:
70720÷884=80
I=80×2500=2,00,000
Sandeep's annual income is ₹2,00,000.
Spending on food = 32% of I
Remaining income after food:
100%−32%=68% of I=0.68I
Spending on travelling = 20% of the remaining income
Remaining income after travelling:
(100%−20%) of 0.68I=80% of 0.68I=0.80×0.68I
Spending on clothes = 35% of the remaining income
Final remaining savings:
(100%−35%) of (0.80×0.68I)=65% of (0.80×0.68I)=0.65×0.80×0.68I
Given that the savings are ₹70,720:
0.65×0.80×0.68×I=70720
100
65
×
100
80
×
100
68
×I=70720
20
13
×
5
4
×
25
17
×I=70720
20×5×25
13×4×17
×I=70720
2500
884
×I=70720
I=
884
70720×2500
Dividing 70720 by 884:
70720÷884=80
I=80×2500=2,00,000
Sandeep's annual income is ₹2,00,000.