Top 10 Model Question Sets ... 247 चाहनासँग \( £ 5000 \) छ। सो दिनमा विनिमय दर \( £ 1= \) रु. 150 र 1 अमेरिकन डलर = रु. 125 रहेको छ । Chahana has £5000. The exchange rate of pound sterling on the day is \( £ 1= \) Rs. 150 and the exchange rate of 1 American dollar \( = \) Rs. 125. (a) खरिददर र बिक्रीदर भन्नाले के बुभिन्छ ? What do you mean by buying rate and selling rate? [1U] (b) \( £ 5000 \) सँग कति अमेरिकन डलर साट्न सकिन्छ ? How many American dollars can be exchanged with \( £ 5000 \) ? [1HA] (c) यदि अमेरिकन डलरको तुलनामा नेपाली मुद्रा \( 5 \% \) ले अवमूल्यन भयो र पाउन्ड स्टर्लिडको तुलनामा चाहि नेपाली मुद्रामा \( 2 \% \) ले अधिमूल्यन भयो भने, पाउन्ड स्टर्लिङको तुलनामा अमेरिकी डलरमा कति प्रतिशतले अवमूल्यन वा अधिमूल्यन भयो ? पत्ता लगाउनुहोस् । If there is \( 5 \% \) devaluation in Nepali currency in comparison to American dollars and \( 2 \% \) revaluation in Nepali currency in comparison to pound sterling, by what percentage is the US dollar revaluated or devaluated in comparison to the pound sterling? Find it. एक जना गणित शिक्षकले आफ्नो कक्षाका प्रत्येक विद्यार्थीलाई वर्गाकार आधार भएको पिरामिड बनाउने प्रयोगात्मक कार्य दिन्छन् । प्रतिभाले आधारको क्षेत्रफल \( 64 \mathrm{~cm}^{2} \) र पूरा सतहको क्षेत्रफल \( 144 \mathrm{~cm}^{2} \) भएको पिरामिड बनार्उंधिन् । नम्रताले भने प्रत्येक किनारा प्रतिभाको भन्दा दोब्बर हुने गरी बनाउँछिन् । A math teacher assigns a practical work of preparing square based pyramid to each student of the class. Prativa prepares a pyramid of base area \( 64 \mathrm{~cm}^{2} \) and total surface area \( 144 \mathrm{~cm}^{2} \). Namrata makes each edge just double of the edges of the pyramid made by Prativa. (a) प्रतिभाको पिरामिडको छड्के सतहको उचाइ पत्ता लगाउनुहोस् । Find the slant height of Prativa's pyramid. [1K] (b) नम्रताको पिरामिडको पूरा सतहको क्षेत्रफल कति होला ? What is the total surface area of Namrata's pyramid? [2U] (c) प्रतिभाले दाबी गई्छिन कि उनको पिरामिडको आयतन नम्रताको पिरामिडको आयतनको \( 25 \% \) छ। के यो सही हो ? होइन भने यो कति प्रतिशत छ ? गणना गरी तय गर्नुहोस् । Prativa claims that the volume of her pyramid is \( 25 \% \) of the volume of the Namrata's pyramid. Is it true? If not, then what percent is it? Decide by calculation. [1HA] एउटा व्यस्त पार्कको एकापट्टि कुनामा एउटा आइसक्रिमको पसल छ। पसलेले उचाइ 7 cm र भित्री आयतन \( 32.34 . \mathrm{cm}^{3} \)

Below are the worked‐out solutions and explanations for each part of the question. ────────────────────────────── 1. Currency Exchange Problem Chahana has £5000 and the given exchange rates are:   • Pound sterling: 1£ = Rs. 150   • US dollar: 1$ = Rs. 125 (a) खरिददर (Buying rate) र बिक्रीदर (Selling rate) भन्नाले तपाईँले एउटा मुलुकको मुद्रा खरिद गर्दा लिने (बैंक वा मुद्रा विनिमयकर्ताद्वारा विदेशी मुद्रा किन्नको लागि लगाइने दर) तथा बेच्दा पाउने दरलाई जनाउँछ ।   In other words, the buying rate is the rate at which the money changer/bank buys the foreign currency from you, and the selling rate is the rate at which they sell the foreign currency to you. (b) How many US dollars can be obtained for £5000?   Step 1. Convert pounds into rupees:     Total rupees = £5000 × Rs.150 = Rs.750,000   Step 2. Convert rupees into US dollars using the dollar rate:     Number of dollars = Rs.750,000 ÷ Rs.125 = 6000 dollars   Therefore, £5000 can be exchanged for 6000 US dollars. (c) Now, suppose there is a 5% devaluation in the Nepali rupee relative to the US dollar and a 2% revaluation in the Nepali rupee relative to the pound sterling. By using the rupee as a common base, we determine the new effective exchange rate between the US dollar and the pound sterling.   Original rates are:     1£ = Rs.150  and  1$ = Rs.125   Thus, originally, 1£ corresponds to 150/125 = 1.2 dollars.   Adjustment details:   • Devaluation vs. US dollar by 5% means that the rupee becomes 5% weaker relative to the dollar. Thus, the rupee amount needed for 1$ increases by 5%:     New rate for 1$ = Rs.125 × 1.05 = Rs.131.25   • Revaluation vs. pound sterling by 2% means that the rupee becomes 2% stronger relative to the pound. Thus, the rupee amount needed for 1£ decreases by 2%:     New rate for 1£ = Rs.150 × 0.98 = Rs.147   Now, the new implicit exchange rate for dollars per pound is:     1£ = Rs.147;  1$ = Rs.131.25   So, in dollars: 1£ = 147 ÷ 131.25 ≈ 1.12 dollars   Change in the dollar value relative to the pound:     Initial: 1.2 dollars; New: 1.12 dollars   The decrease = 1.2 – 1.12 = 0.08 dollars   Percentage decrease = (0.08 ÷ 1.2) × 100 ≈ 6.67 %   Thus, relative to the pound sterling, the US dollar has depreciated by approximately 6.67%. ────────────────────────────── 2. Pyramid Construction Problem Prativa’s pyramid has a square base with a base area of 64 cm² and a total surface area of 144 cm². Namrata makes a similar pyramid but with every edge exactly double that of Prativa’s pyramid. Let’s denote:   s = side of the base of Prativa’s pyramid. Since the base area = s², we have:   s² = 64 ⟹ s = 8 cm For a square-based pyramid, the total surface area (TSA) is given by:   TSA = Base area + Lateral surface area   For the lateral surface area, note that there are 4 identical triangles. A convenient formula is:     Lateral area = ½ × perimeter × slant height = ½ × (4s) × l = 2s × l So,   Base area + 2s·l = 144 Substitute s = 8 and Base area = 64:   64 + 16l = 144 Solve for l:   16l = 144 – 64 = 80   l = 80 ÷ 16 = 5 cm (a) The slant height of Prativa’s pyramid is 5 cm. (b) Namrata’s pyramid has every edge doubled. For similar solids, a doubling of every linear dimension means:   – The base side becomes 2 × 8 = 16 cm, so the new base area = 16² = 256 cm².   – In general, all surface areas scale by the square of the scale factor. Since the scale factor is 2, the total surface area of Namrata’s pyramid is:     New TSA = (Scale factor)² × (Original TSA) = 2² × 144 = 4 × 144 = 576 cm². (c) Prativa claims that the volume of her pyramid is 25% of Namrata’s pyramid’s volume. Let’s verify this by considering the scaling for volumes.   For similar solids, volumes scale by the cube of the linear dimension scale factor. Here, with a scale factor of 2:     Volume ratio = 1 ÷ (2³) = 1 ÷ 8 = 12.5% That is, Prativa’s pyramid’s volume is 12.5% of Namrata’s pyramid’s volume—not 25%. ────────────────────────────── 3. Ice Cream Shop (Incomplete Information) The last part of the question states:   "एउटा व्यस्त पार्कको एकापट्टि कुनामा एउटा आइसक्रिमको पसल छ। पसलेले उचाइ 7 cm र भित्री आयतन 32.34 cm³"   "In a busy park, at one corner, there is an ice cream shop. The shop has a height of 7 cm and an internal volume of 32.34 cm³." At this point, the problem statement does not include a question (e.g. to find the base area, dimensions, or any other detail). Additional information or a specific question is needed to proceed with a corresponding calculation. ────────────────────────────── Summary of Answers: 1. Currency Problem   (a) The buying rate is the rate at which a bank/money changer buys foreign currency from the customer, whereas the selling rate is the rate at which the bank/money changer sells the foreign currency.   (b) £5000 can be exchanged for 6000 US dollars.   (c) Relative to the pound sterling, the US dollar depreciates by approximately 6.67%. 2. Pyramid Problem   (a) The slant height of Prativa’s pyramid is 5 cm.   (b) The total surface area of Namrata’s pyramid is 576 cm².   (c) In actuality, the volume of Prativa’s pyramid is 12.5% of Namrata’s pyramid’s volume (not 25%). 3. Ice Cream Shop Problem   Additional details are needed as the question is incomplete. These are the complete detailed solutions based on the provided information.