Mathematics Set 10

Question 1

पाँच वर्षको अवधिमा कम्पनीले तलबको कति प्रतिशत भत्ता दिएको रहेछ ?

Accepted Answer

undefined — पाँच वर्षको कुल तलब १७१० र कुल भत्ता १७ हुन्छ । (१७ / १७१०) * १०० गर्दा लगभग १ प्रतिशत हुन आउँछ ।

Question 2

पहिलो प्रकारको चामलको प्रति केजी १५ रुपैयाँ पर्छ । दोस्रो प्रकारको चामललाई प्रति केजी २० रुपैयाँ पर्छ । ती दुई प्रकारको चामललाई २:३ को अनुपातमा मिसाइयो भने मिश्रणको मूल्य कति पर्ला ? (The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:)

Accepted Answer

undefined — Weighted average price = (Price1 × Ratio1 + Price2 × Ratio2) / (Total Ratio) = (15 × 2 + 20 × 3) / (2 + 3) = (30 + 60) / 5 = 90 / 5 = 18.

Question 3

कुनै विद्यार्थीको अंक ६३ हुनु पर्नेमा गल्तीवश ८३ राखियो, जसले कक्षाको औसत अंकमा आधाले वृद्धि भयो भने सो कक्षामा जम्मा कति विद्यार्थी रहेछन् ? (A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:)

Accepted Answer

undefined — अङ्कको फरक = ८३ - ६३ = २०। औसत वृद्धि १/२ भएकोले, विद्यार्थी संख्या (n) × १/२ = २० हुन्छ, जसबाट n = ४० प्राप्त हुन्छ।

Question 4

A ले कुनै काम १५ दिनमा र B ले उक्त काम २० दिनमा गर्न सक्छ। यदि दुवै जना सँगै मिलेर ४ दिनसम्म काम गर्दा अब कति काम बाँकी रहन्छ ? A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

Accepted Answer

undefined — (A+B) को १ दिनको काम = 1/15 + 1/20 = 7/60 हुन्छ। ४ दिनको जम्मा काम = 4 * (7/60) = 7/15। बाँकी काम = 1 - 7/15 = 8/15।

Question 5

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

Accepted Answer

undefined — Let perimeter be P, length L, and breadth B. Given P:B = 5:1, so 2(L+B)/B = 5, which leads to 2L = 3B or L = 1.5B. Area L*B = 1.5B^2 = 216, so B^2 = 144 and B = 12 cm. Length L = 1.5 * 12 = 18 cm.

Question 6

१३० मिटर लामो रेलले ४५ किलोमिटर प्रतिघण्टाका दरले ३० सेकेण्डमा पार गर्छ भने उक्त पुलको लम्बाई कति होला ? (The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:)

Accepted Answer

undefined — रेलको गति मिटर/सेकेण्डमा १२.५ हुन्छ । ३० सेकेण्डमा रेलले ३७५ मिटर दुरी तय गर्छ, जसमा रेलको लम्बाई १३० मिटर घटाउँदा पुलको लम्बाई २४५ मिटर हुन्छ ।

Question 7

The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:

Accepted Answer

undefined — Using formula TD = (BD * 100) / (100 + RT), where R=15, T=4/12=1/3. TD = (420 * 100) / (100 + 15*1/3) = 42000 / 105 = 400.

Question 8

The sum of first five prime numbers is:

Accepted Answer

undefined — The first five prime numbers are 2, 3, 5, 7, and 11. Their sum is 2 + 3 + 5 + 7 + 11 = 28.

Question 9

तीनवटा पाईपहरु क्रमशः A, B, C ले एउटा खालि ट्याङ्कि भर्न क्रमशः ३० मिनेट, २० मिनेट र १० मिनेट लगाउँछन् । भने तीन वटा पाईप खोल्दा ट्याङ्कि कति समयमा भरिन्छ? (Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened.)

Accepted Answer

undefined — संयुक्त कार्यदर = 1/30 + 1/20 + 1/10 = (2+3+6)/60 = 11/60। समय = ६०/११ = ५ ५/११ मिनेट। विकल्प 'A' मा ५ पूर्णाङ्क छुटेको देखिन्छ।

Question 10

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw ?

Accepted Answer

undefined — Total balls = 2+3+4 = 9. Total ways to draw 3 balls = 9C3 = 84. Ways with no black balls (selecting from 6 white/red balls) = 6C3 = 20. Ways with at least one black ball = 84 - 20 = 64.

Mathematics — Set 10

पाँच वर्षको अवधिमा कम्पनीले तलबको कति प्रतिशत भत्ता दिएको रहेछ ?

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The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

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The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:

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The sum of first five prime numbers is:

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A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw ?

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