सविस्तर स्पष्टीकरण (Detailed Explanation):
अचूक उत्तर: पर्याय (1)
दिलेल्याप्रमाणे:
एका व्यक्तीचे मासिक उत्पन्न 80,000 रुपये आहे.
मासिक खर्च 45,000 रुपये आहे
उत्पन्न 16% ने वाढले.
खर्च 8% ने वाढला.
वापरलेले सूत्र:
उत्पन्न = खर्च + बचत
गणना:
उत्पन्न 16% ने वाढले = 80000 x 116/100 = 92800
खर्च 8% ने वाढला = 45000 x 108/100 = 48600
जुनी बचत = 80000 - 45000 = 35000
नवीन बचत = 92800 - 48600 = 44200
वाढवा = 44200 - 35000 = 9200
टक्केवारी वाढ = 9200/35000 x 100 = 9200/350 = 26.28%
∴ बरोबर उत्तर 26.28% आहे.
Shortcut Trick
Ratio of Income : Expenditure : Savings = 80,000 : 45,000 : 35,000 = 16 : 9 : 7
Total units of Income Increase = 16 × 16% = 256
Total units of Expenditure Increase = 9 × 8% = 72
Total units of Savings Increase = 256 − 72 = 184
Percentage Increase in Savings = 184 ÷ 7 ≈ 26.29%
∴ The correct answer is 26.29%.
Alternate Method
Given: Monthly Income = ₹80,000, Monthly Expenditure = ₹45,000
Formula Used: Savings = Income − Expenditure; % Increase = (Change ÷ Original) × 100
⇒ Original Savings = 80,000 − 45,000 = ₹35,000
⇒ Increase in Income = 16% of 80,000 = ₹12,800
⇒ Increase in Expenditure = 8% of 45,000 = ₹3,600
⇒ Increase in Savings = 12,800 − 3,600 = ₹9,200
⇒ Percentage Increase in Savings = (9,200 ÷ 35,000) × 100
⇒ % Increase = 920 ÷ 35 ≈ 26.2857%
∴ The correct answer is 26.29%.
Related Concepts:
Fundamental Income Identity
Total Income is always the sum of Expenditure and Savings (I = E + S). Any change in Income must be balanced by changes in E and S.
Weighted Average Method
Income % change = (Exp Ratio × Exp % change + Savings Ratio × Savings % change) ÷ (Exp Ratio + Savings Ratio).
Percentage Change Formula
Percentage Change = [(Final Value − Initial Value) ÷ Initial Value] × 100.
स्पष्टीकरण आकृती (Solution Visual Diagram):
Solution Diagram