Mathematics Set 9

Question 1

A,B,C ले कुनै व्यवसायमा ५०,००० लगानी गरे । A ले B ले भन्दा ४००० बढि लगानी गर्यो र B ले C भन्दा ५००० बढि लगानी गर्यो, भने जम्मा नाफा ३५००० हुँदा भने A ले कति प्राप्त गर्ला ?

A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:

Accepted Answer

undefined — Let C=x. B=x+5000, A=x+9000. Total x + (x+5000) + (x+9000) = 50000 gives x=12000. Ratio A:B:C = 21:17:12. A's profit = (21/50) * 35000 = 14700.

Question 2

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

Accepted Answer

undefined — Let the team average be x. Total age = 11x. Captain = 26, Wicket keeper = 29. Excluding them, sum = 11x - 55. Average of 9 players = (11x - 55)/9 = x - 1. Solving 11x - 55 = 9x - 9 gives 2x = 46, so x = 23 years.

Question 3

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Accepted Answer

undefined — Select 3 consonants from 7 (7C3 = 35) and 2 vowels from 4 (4C2 = 6). Total selections = 35 * 6 = 210. These 5 letters can be arranged in 5! (120) ways. Total words = 210 * 120 = 25200.

Question 4

तल दिइएका कुन वर्षमा दुई ओटा कम्पनीको उत्पादनमा अधिकतम फरक देखिन्छ ? In which of the following years, the difference between the productions of Companies X and Y was the maximum among the given years ?

Accepted Answer

undefined — वर्ष २००० मा कम्पनी X को ७८ र Y को १२८ उत्पादन छ, जसको फरक ५० हजार छ। यो अन्य वर्षहरूको तुलनामा सबैभन्दा धेरै हो।

Question 5

The square root of (7 + 3√5) (7 - 3√5) is

Accepted Answer

undefined — Using (a+b)(a-b) = a² - b², we get 7² - (3√5)² = 49 - 45 = 4. The square root of 4 is 2.

Question 6

हवाइजहाजले केही दूरी ५ घण्टामा २४० किमी प्रति घण्टाको दरले पार गर्दछ । सोही दुरी १ २/३ घण्टामा पार गर्न कति वेग हुनुपर्दछ ?

Accepted Answer

undefined — दूरी = चाल x समय = २४० x ५ = १२०० किमी। नयाँ समय = १ २/३ = ५/३ घण्टा। नयाँ चाल = १२०० / (५/३) = ७२० किमी प्रति घण्टा।

Question 7

१ देखि ७० सम्मका संख्याहरुमा अन्त्यमा १ वा ९ आउने सङ्ख्या कति प्रतिशत हो ? (What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?)

Accepted Answer

undefined — १ देखि ७० सम्ममा एकाई स्थानमा १ वा ९ आउने संख्याहरु (१, ९, ११, १९, २१, २९, ३१, ३९, ४१, ४९, ५१, ५९, ६१, ६९) गरी जम्मा १४ वटा छन्। यसको प्रतिशत निकाल्दा (१४/७०) x १०० = २०% हुन्छ।

Question 8

५ वजेर १५ मिनेटमा कति डिग्रीको कोण बन्छ ?
At what angle the hands of a clock are inclined at 15 minutes past 5?

Accepted Answer

undefined — Using the formula Angle = |30H - (11/2)M|, where H=5 and M=15: |30(5) - (11/2)15| = |150 - 82.5| = 67.5°, which is 67(1/2)°.

Question 9

७ ओटा माकुराले ७ दिनमा ७ ओटा जाल बनाउँछन् भने एउटा माकुराले एउटा जाल बनाउन कति दिन लगाउँला ? / If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

Accepted Answer

undefined — ७ माकुराले ७ दिनमा ७ जाल बनाउँछन् भने १ माकुराले १ जाल बनाउन पनि ७ दिन नै लाग्छ। सूत्र: (M1*D1)/W1 = (M2*D2)/W2 प्रयोग गर्दा (7*7)/7 = (1*D)/1, जहाँ D=7 प्राप्त हुन्छ।

Question 10

राम र हरीको तलबको अनुपात २:३ थियो । यदि उनीहरुको तलव रु. ४००० ले बढ्दा तलवको अनुपात ४०:५७ भयो भने हरीको तलव कति होला ? (Salaries of Ram and Hari are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Hari's salary?)

Accepted Answer

undefined — समीकरण (2x + 4000) / (3x + 4000) = 40 / 57 बाट x = 68000/6 निस्कन्छ। हरीको नयाँ तलब = 3x + 4000 = 34000 + 4000 = 38000 हुन्छ।

Mathematics — Set 9

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The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

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Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

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The square root of (7 + 3√5) (7 - 3√5) is

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१ देखि ७० सम्मका संख्याहरुमा अन्त्यमा १ वा ९ आउने सङ्ख्या कति प्रतिशत हो ? (What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?)

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५ वजेर १५ मिनेटमा कति डिग्रीको कोण बन्छ ? At what angle the hands of a clock are inclined at 15 minutes past 5?

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