Top 10 Model Question Sets ... 24 चाहनासँग $$ £ 5000 $$ छ । सो दिनमा विनिमय दर $$ £ 1= $$ रु. 150 र 1 अमेरिकन डलर $$ = $$ ₹. 125 रहेको छ । Chahana he £5000. The exchange rate of pound sterling on the day is $$ £ 1= $$ Rs. 150 and the exchange rate of 1 America dollar $$ = $$ Rs. 125. (a) खरिददर र बिक्रीदर भन्नाले के बुभिन्छ? What do you mean by buying rate and selling rate? [11 (b) $$ £ 5000 $$ सँग कति अमेरिकन डलर साट्न सकिन्छ ? How many American dollars can be exchanged with $$ £ 5000 $$ $$ [1 \mathrm{H}] $$ (c) यदि अमेरिकन डलरको तुलनामा नेपाली मुद्रा $$ 5 \% $$ ले अवमूल्यन भयो र पाउन्ड स्टर्लिडको तुलनामा चाहि नेपाली मुद्राम $$ 2 \% $$ ले अधिमूल्यन भयो भने, पाउन्ड स्टर्लिङको तुलनामा अमेरिकी डलरमा कति प्रतिशतले अवमूल्यन वा अधिमूल्य भयो ? पत्ता लगाउनुहोस् । If there is $$ 5 \% $$ devaluation in Nepali currency in comparison to American dollars an $$ 2 \% $$ revaluation in Nepali currency in comparison to pound sterling, by what percentage is the US dolla revaluated or devaluated in comparison to the pound sterling? Find it. [21 एक जना गणित शिक्षकले आफ्नो कक्षाका प्रत्येक विद्यार्थीलाई वर्गाकार आधार भएको पिरामिड बनाउने प्रयोगात्मक का दिन्छन् । प्रतिभाले आधारको क्षेत्रफल $$ 64 \mathrm{~cm}^{2} $$ र पूरा सतहको क्षेत्रफल $$ 144 \mathrm{~cm}^{2} $$ भएको पिरामिड बनार्डधिन् । नम्रताले भं प्रत्येक किनारा प्रतिभाको भन्दा दोब्बर हुने गरी बनाउँछिन् । A math teacher assigns a practical work of preparing squar 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. (b) नम्रताको पिरामिडको पूरा सतहको क्षेत्रफल कति होला ? What is the total surface area of Namrata's pyramid? \{2U (c) प्रतिभाले दाबी गर्छिन 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 $$ 32.34 . \mathrm{cm} $$

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Let's break down the problem step by step.

### Part 1: Currency Exchange

#### (a) खरिददर र बिक्रीदर भन्नाले के बुभिन्छ?
**Buying Rate** (खरिददर) refers to the rate at which a bank or financial institution buys foreign currency from customers.  
**Selling Rate** (बिक्रीदर) refers to the rate at which the bank sells foreign currency to customers.

#### (b) $$ £ 5000 $$ सँग कति अमेरिकन डलर साट्न सकिन्छ?
To find out how many American dollars can be exchanged for $$ £ 5000 $$, we first need to convert pounds to rupees and then rupees to dollars.

1. Convert $$ £ 5000 $$ to rupees:
   $$
   \text{Rupees} = £ 5000 \times 150
   $$

2. Convert rupees to American dollars:
   $$
   \text{Dollars} = \frac{\text{Rupees}}{125}
   $$

Let's calculate this step by step.

1. Calculate rupees:
   $$
   \text{Rupees} = 5000 \times 150 = 750000
   $$

2. Calculate dollars:
   $$
   \text{Dollars} = \frac{750000}{125} = 6000
   $$

So, $$ £ 5000 $$ can be exchanged for **6000 American dollars**.

#### (c) पाउन्ड स्टर्लिङको तुलनामा अमेरिकी डलरमा कति प्रतिशतले अवमूल्यन वा अधिमूल्य भयो?
To find the percentage change in the value of the US dollar compared to the pound sterling, we need to consider the changes in the exchange rates due to the devaluation and revaluation of the Nepali currency.

1. **Initial exchange rates:**
   - $$ £ 1 = ₹ 150 $$
   - $$ 1 \text{ USD} = ₹ 125 $$

2. **After changes:**
   - Nepali currency devaluates by $$ 5\% $$ against USD:
     $$
     \text{New USD rate} = 125 \times (1 + 0.05) = 125 \times 1.05 = 131.25
     $$
   - Nepali currency revaluates by $$ 2\% $$ against GBP:
     $$
     \text{New GBP rate} = 150 \times (1 - 0.02) = 150 \times 0.98 = 147
     $$

3. **New exchange rates:**
   - $$ 1 \text{ USD} = ₹ 131.25 $$
   - $$ £ 1 = ₹ 147 $$

4. **Calculate the new exchange rate of USD to GBP:**
   $$
   \text{New USD to GBP rate} = \frac{131.25}{147}
   $$

5. **Calculate the percentage change:**
   - Original USD to GBP rate:
     $$
     \text{Original rate} = \frac{125}{150} = \frac{5}{6} \approx 0.8333
     $$
   - New USD to GBP rate:
     $$
     \text{New rate} = \frac{131.25}{147} \approx 0.8947
     $$
   - Percentage change:
     $$
     \text{Percentage change} = \left( \frac{0.8947 - 0.8333}{0.8333} \right) \times 100
     $$

Let's calculate the percentage change.

1. Calculate the difference:
   $$
   0.8947 - 0.8333 = 0.0614
   $$

2. Calculate the percentage change:
   $$
   \text{Percentage change} = \left( \frac{0.0614}{0.8333} \right) \times 100 \approx 7.37\%
   $$

Thus, the US dollar has appreciated by approximately **7.37%** against the pound sterling.

### Part 2: Pyramid Problem

#### (a) प्रतिभाको पिरामिडको छड्के सतहको उचाइ पत्ता लगाउनुहोस्।
Given:
- Base area $$ A = 64 \, \text{cm}^2 $$
- Total surface area $$ S = 144 \, \text{cm}^2 $$

1. The base side length $$ a $$ can be calculated from the area:
   $$
   a^2 = 64 \implies a = 8 \, \text{cm}
   $$

2. The total surface area of a square pyramid is given by:
   $$
   S = A + \frac{1}{2} \times \text{perimeter} \times \text{slant height}
   $$
   The perimeter $$ P $$ of the base is:
   $$
   P = 4a = 4 \times 8 = 32 \, \text{cm}
   $$

3. Substitute into the total surface area formula:
   $$
   144 = 64 + \frac{1}{2} \times 32 \times l
   $$
   Simplifying gives:
   $$
   144 - 64 = 16l \implies 80 = 16l \implies l = 5 \, \text{cm}
   $$

So, the slant height of Prativa's pyramid is **5 cm**.

#### (b) नम्रताको पिरामिडको पूरा सतहको क्षेत्रफल कति होला?
Namrata's pyramid has edges that are double the length of Prativa's pyramid.

1. The base side length of Namrata's pyramid:
   $$
   a' = 2a = 2 \times 8 = 16 \, \text{cm}
   $$

2. The base area of Namrata's pyramid:
   $$
   A' = (a')^2 = 16^2 = 256 \, \text{cm}^2
   $$

3. The new slant height $$ l' $$ will also be doubled:
   $$
   l' = 2l = 2 \times 5 = 10 \, \text{cm}
   $$

4. The perimeter of the base of Namrata's pyramid:
   $$
   P' = 4a' = 4 \times 16 = 64 \, \text{cm}
   $$

5. Total surface area of Namrata's pyramid:
   $$
   S' = A' + \frac{1}{2} \times P' \times l' = 256 + \frac{1}{2} \times 64 \times 10
   $$
   $$
   S' = 256 + 320 = 576 \, \text{cm}^2
   $$

So
**Part 1: Currency Exchange** (a) **Buying Rate** is the rate at which a bank buys foreign currency from customers, and **Selling Rate** is the rate at which the bank sells foreign currency to customers. (b) $$ £ 5000 $$ can be exchanged for **6000 American dollars**. (c) The US dollar has **appreciated by approximately 7.37%** against the pound sterling. **Part 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) Prativa's pyramid's volume is **not** $$ 25\% $$ of Namrata's pyramid's volume. Instead, it is approximately **16.67%** of Namrata's volume.

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