38 CHAP - 38. PIE-CHARTS IMPORTANT FACTS AND FORMULAE The...

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38. PIE-CHARTS IMPORTANT FACTS AND FORMULAE The pie-chart or a pie-graph is a method of representing a given numerical data in the form of sectors of a circle. The sectors of the circle are constructed in such a way that the area of each sector is proportional to the corresponding value of the component of the data. From geometry, we know that the area of a circle is proportional to the central angle. So, the central angle of each sector must be proportional to the corresponding value of the component. Since the sum of all the central angle is 360°, we have Value of the component ° Central angle of the component = ------------------------ * 360 Total value SOLVED EXAMPLES The procedure of solving problems based on pie-charts will be clear from the following solved examples. Example 1. The following pie-chart shows the sources of funds to be collected by the National Highways Authority of India (NHAI) for its Phase II projects. Study the pie-chart and answer the questions that follow. SOURCES OF FUNDS TO BE ARRANGED BY NHAI FOR PHASE II PROJECTS (IN CRORES RS.)
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1. Near about 20% of the funds are to be arranged through: (a) SPVS (b) External Assistance (c) Annuity (d) Market Borrowing 2. The central angle corresponding to Market Borrowing is: (a) 52° (b) 137.8° (c) 187.2° (d) 192.4° 3. The approximate ratio of the funds to be arranged through Toll and that through Market Borrowing is: (a) 2:9 (b) 1:6 (c) 3:11 (d) 2:5 4. If NHAI could receive a total of Rs. 9695 crores as External Assistance, by what percent (approximately) should it increase the Market Borrowings to arrange for the shortage of funds ? (a) 4.5% (b) 7.5% (c) 6% (d) 8% 5.If the toll is to be collected through an outsourced agency by allowing a maximum 10% commission, how much amount should be permitted to be collected by the outsourced agency, so that the project is supported with Rs. 4910 crores ? (a) Rs.6213 crores (b) Rs. 5827 crores (c) Rs. 5401 crores (d) Rs. 5216 crores SOLUTION 1. (b): 20% of the total funds to be arranged = Rs.(20% of 57600) crores = Rs.11520 crores Rs.11486 crores. 2. (c):Central angle corresponding to Market Borrowing = 29952 -------- * 360 ° 57600 = 187.2 ° 3. (b): 4910 1 1 Required ratio = ------- = ---- = ---- 29952 6.1 6 4. (c):Shortage of funds arranged through External Assistance =Rs.(11486-9695) crores =Rs. 1791 crores. therefore, Increase required in Market Borrowings =Rs. 1791 crores. 1791
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38 CHAP - 38. PIE-CHARTS IMPORTANT FACTS AND FORMULAE The...

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