Mathematics Set 8

Question 1

एउटा दुध पसलेसँग २ क्यान दुध छ, जसमा पहिलो क्यानमा २५ प्रतिशत पानी र बाँकी दुध छ । दोस्रो भाँडोमा ५० प्रतिशत पानी छ । १२ लिटर दुधमा पानी र दुधको अनुपात ३ः५ पुर्याउन प्रत्येक क्यानबाट कति दुध मिसाउनु पर्ला ?

A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

Accepted Answer

6 litres, 6 litres — Using allegation/mixture method: Required water is 3/8 = 37.5%. Mixing 25% and 50% to get 37.5% gives a ratio of (50-37.5):(37.5-25) = 12.5:12.5 = 1:1. For 12 litres, 6 litres each are needed.

Question 2

एउटा किराना पसलेले पाँच महिनामा क्रमशः Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 को सामान बिक्री गर्‍यो भने सबै महिनाको औसत रु. ६५०० कायम गर्न छैटौं महिनामा कतिको सामान बेच्नु पर्ला ? / A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

Accepted Answer

Rs. 4991 — The total sale required for 6 months to have an average of 6500 is 6500 * 6 = 39,000. Sum of sales for the first 5 months = 6435 + 6927 + 6855 + 7230 + 6562 = 34,009. Required sale in the 6th month = 39,000 - 34,009 = 4,991.

Question 3

एउटा व्याट्सम्यानले ११० रन बनायो जसमा ८ छक्का र ३ चौका हान्यो भने कति प्रतिशत रन दुई विकेटका विचमा दौडेर बनायो ?

A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

Accepted Answer

45 5/11 % — Boundary runs = (3*4) + (8*6) = 12 + 48 = 60. Running runs = 110 - 60 = 50. Percent = (50/110) * 100 = 45 5/11 %.

Question 4

किताबको अंकित मूल्य लागत मूल्यको बीस प्रतिशत बढी निर्धारण गरिएको छ । यदि किताबको अंकित मूल्य रु. १८० निर्धारण गरिएको छ भने सो किताब प्रकाशन गर्दा कागजमा कति खर्च भएको होला ? / The price of the book is marked 20% above the C.P. If the marked price of the book is Rs. 180, then what is the cost of the paper used in a single copy of the book?

Accepted Answer

Rs. 37.50 — Marked Price (120%) = 180, so C.P. (100%) = 180/1.2 = 150. Paper cost is 25% of C.P., which is 0.25 * 150 = Rs. 37.50.

Question 5

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

23 years — 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 6

यदि A ले B लाई ५००० रुपैयाँ दुई वर्षको लागि र C लाई ३००० रुपैयाँ ४ वर्षको लागि साधारण व्याजमा समान व्याजदरमा ऋण दिएको रहेछ । उसले एकमुष्ट रुपमा २२०० रुपैयाँ साधारण व्याज प्राप्त गरेछ भने वार्षिक व्याजदर कति होला ? (A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:)

Accepted Answer

10% — B बाट प्राप्त व्याज (5000 * 2 * R)/100 = 100R र C बाट (3000 * 4 * R)/100 = 120R हुन्छ। जम्मा व्याज 220R = 2200 हुँदा R = 10% हुन्छ।

Question 7

एउटा बैंकले ५ प्रतिशत अर्धवार्षिक चक्रिय व्याजको व्यवस्था गरेको छ । यदि एउटा ग्राहकले हरेक जनवरी १ र जुलाई १ मा रु. १६०० जम्मा गर्छ भने व्याजका रुपमा उसले वार्षिक कति रकम पाउँछ ? (A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:)

Accepted Answer

Rs. 121 — वार्षिक ५ प्रतिशत ब्याजदरलाई अर्धवार्षिक रूपमा गणना गर्दा ६ महिनाको ब्याजदर २.५ प्रतिशत हुन्छ। जनवरी १ मा जम्मा गरेको रु १६०० ले दुई किस्ता (वर्षभरि) ब्याज पाउँछ भने जुलाई १ मा जम्मा गरेको रकमले एक किस्ता ब्याज पाउँछ, जसको कुल जोड रु १२१ हुन्छ।

Question 8

The value of ((0.96)^3 - (0.1)^3) / ((0.96)^2 + 0.096 + (0.1)^2) is:

Accepted Answer

0.86 — Using the algebraic formula (a^3 - b^3) / (a^2 + ab + b^2) = (a - b). Here, a = 0.96 and b = 0.1, so 0.96 - 0.1 = 0.86.

Question 9

मान्छे र उसको बहावको गति सँगसँगै १५ किलोमिटर प्रतिघण्टा छ। यदि बहावको गति २.५ किलोमिटर प्रति घण्टा हो, भने बहावको उल्टो दिशामा मानिसको गति कति होला ? / A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

Accepted Answer

10 km/hr — Speed with current (downstream) = Man's speed in still water + Current speed. So, 15 = u + 2.5, which gives u = 12.5 km/hr. Speed against current (upstream) = u - current speed = 12.5 - 2.5 = 10 km/hr.

Question 10

एउटा रेलले ६० किलोमिटर प्रतिघण्टाको गतिमा दौडिदा ९ सेकेण्डमा एउटा खम्बा पार गर्छ भने उक्त रेलको लम्बाई कति होला ? A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

Accepted Answer

150 metres — Speed = 60 km/hr = 60 * (5/18) m/s = 50/3 m/s. Length = Speed * Time = (50/3) * 9 = 150 metres.

Mathematics — Set 8

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Questions

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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The value of ((0.96)^3 - (0.1)^3) / ((0.96)^2 + 0.096 + (0.1)^2) is:

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