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Mathematics — Set 5

10 Questions with Answers & Explanations

Set 5 of 14

1

बिक्री मूल्यलाई दोब्बर बनाउँदा नाफा तेब्बर हुन्छ भने नाफा प्रतिशत कति हो ? / If selling price is doubled, the profit triples. Find the profit percent.

Options

A

66 2/3

B

100

C

105 1/3

D

120

Correct Answer

100

Explanation

मानौँ लागत मूल्य x र बिक्री मूल्य y छ । नाफा = y - x । नयाँ बिक्री मूल्य २y हुँदा नाफा २y - x हुन्छ । समीकरण: २y - x = ३(y - x) => y = २x । नाफा = २x - x = x । नाफा प्रतिशत = (x/x) * १०० = १००% ।

2

एउटै गतिमा काम गर्दा ६ उस्तै प्रकारका मेसिनले २७० बोतल प्रति मिनेट उत्पादन गर्छन् भने यहि दरमा १० वटा मेसिनले ४ मिनेटमा कति बोतल उत्पादन गर्छन् ? / Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Options

A

648

B

1800

C

2700

D

10800

Correct Answer

1800

Explanation

६ वटा मेसिनले १ मिनेटमा २७० बोतल बनाउँछन्, त्यसैले १ मेसिनले १ मिनेटमा ४५ (२७०/६) बोतल बनाउँछ। १० वटा मेसिनले १ मिनेटमा ४५० र ४ मिनेटमा १८०० बोतल उत्पादन गर्छन्।

3

समान गतिमा ६ ओटा एकै खालका मेसिन चलाउँदा एक मिनेटमा २७० ओटा बोतल उत्पादन गर्न सकिन्छ । त्यहि गतिमा उस्तै खालका १० ओटा मेसिन चलाउँदा ४ मिनेटमा कति बोतल उत्पादन गर्न सकिन्छ ? (Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?)

Options

A

648

B

1800

C

2700

D

10800

Correct Answer

1800

Explanation

One machine produces 270/6 = 45 bottles/min. 10 machines produce 450 bottles/min. In 4 minutes, 10 machines produce 450 * 4 = 1800 bottles.

4

तलका मध्ये कुन विकल्प गलत छ ? Which of the following statements is not correct?

Options

A

log10 10 = 1

B

log (2 + 3) = log (2 x 3)

C

log10 1 = 0

D

log (1 + 2 + 3) = log 1 + log 2 + log 3

Correct Answer

log (2 + 3) = log (2 x 3)

Explanation

Logarithmic laws state that log(a*b) = log a + log b. Therefore, log(2*3) equals log 2 + log 3, not log(2+3). Statement D is correct because 1+2+3 = 6 and 1*2*3 = 6, making log(1+2+3) = log(1*2*3).

5

कुन कम्पनीको पाँच वर्षको औषत उत्पादन सबैभन्दा बढि छ ? The average production for five years was maximum for which company?

Context: तल दिइएको स्तम्भ चित्रमा तीन ओटा कम्पनी X, Y, Z ले दिइएका वर्षहरुमा उत्पादन गरेको कागज ( लाख टन ) मा प्रस्तुत गरिएको छ : The bar graph given below shows the data of the production of paper (in lakh tonnes) by three different companies X, Y and Z over the years. Production of Paper (in lakh tonnes) by Three Companies X, Y and Z over the Years. बाँयाबाट क्रमशः X, Y, Z का स्तम्भ हुन्।

Questions

A

X

B

Y

C

Z

D

X and Z both

Correct Answer

X and Z both

Explanation

कम्पनी X को कुल उत्पादन = ३०+४५+२५+५०+४० = १९०। कम्पनी Y को कुल उत्पादन = २५+३५+३५+४०+५० = १८५। कम्पनी Z को कुल उत्पादन = ३५+४०+४५+३५+३५ = १९०। X र Z दुबैको उत्पादन अधिकतम र समान (१९० लाख टन) छ।

6

कुनै लेखहरू रु १९२० मा वेच्दा जती प्रतिशत नाफा हुन्छ सोहि लेखहरु रु. १२८० मा बेच्दा त्यति प्रतिशत नोक्सान हुन्छ भने उक्त लेखहरुलाई २५ प्रतिशत नाफामा वेच्दा कतिमा वेच्नुपर्छ ?

Options

A

Rs. 2000

B

Rs. 2200

C

Rs. 2400

D

Data inadequate

Correct Answer

Rs. 2000

Explanation

Since profit % equals loss %, the Cost Price (CP) is the average of the two selling prices: (1920 + 1280) / 2 = 1600. To make a 25% profit, the selling price should be 1600 + (25% of 1600) = 1600 + 400 = 2000.

7

तलकामध्ये कुन जोडा वर्षमा उत्तीर्ण परिक्षार्थीहरुको संख्या बराबर छ ? (In which pair of years was the number of candidates qualified, the same?)

Context: तल दिइएको रेखा चित्रमा १९९४ देखि २००० सम्मको सात वर्षको अवधिमा कुनै परिक्षामा सहभागी भई उत्तीर्ण भएका परिक्षार्थीहरुको प्रतिशत प्रस्तुत गरिएको छ। The following line graph gives the percentage of the number of candidates who qualified an examination out of the total number of candidates who appeared for the examination over a period of seven years from 1994 to 2000. Percentage of Candidates Qualified to Appeared in an Examination Over the Years

Questions

A

1995 and 1997

B

1995 and 2000

C

1998 and 1999

D

Data inadequate

Correct Answer

Data inadequate

Explanation

विभिन्न वर्षहरूमा उत्तीर्ण भएका विद्यार्थीहरूको प्रतिशत दिइएको भए तापनि सहभागी संख्या (total appeared) नदिइएकाले कुन वर्षमा बराबर संख्यामा उत्तीर्ण भए भन्न सकिँदैन।

8

पति, पत्नी र उनीहरुको बच्चाको तीन वर्ष अघिको औषत अमेर २७ वर्ष थियो। पत्नी र बच्चाको ५ वर्ष अघिको औषत उमेर २० वर्ष थियो भने पतिको हालको उमेर कति होला ? (The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:)

Options

A

35 years

B

40 years

C

50 years

D

None of these

Correct Answer

40 years

Explanation

Present sum of H+W+C = (27*3) + (3*3) = 81+9 = 90. Present sum of W+C = (20*2) + (5*2) = 40+10 = 50. Present age of husband = 90 - 50 = 40 years.

9

एउटा भाँडो तरल पदार्थले भरिएको छ जसमा ३ भाग पानी र ५ भाग जुस छ भने उक्त मिश्रणमा पानी र जुसको मात्रा बराबर बनाउन कति मिश्रण झिक्नु पर्ला ? (A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?)

Options

A

1/3

B

1/4

C

1/5

D

1/7

Correct Answer

1/5

Explanation

To change the ratio from 3:5 to 1:1, we calculate the replacement required. Using the formula [1/2 * (difference in ratio parts) / (larger part)], we get [1/2 * (5-3) / 5] = 1/5.

10

एउटा खराब दुध व्यापारीले पानी मिसाएर २५ प्रतिशत नाफा गर्ने गरी किनेकै मूल्यमा दुध बेच्दो रहेछ भने कति प्रतिशत पानी मिसाएको रहेछ ? (A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25 %. The percentage of water in the mixture is:)

Options

A

4%

B

6 1/4 %

C

20%

D

25%

Correct Answer

20%

Explanation

To gain 25% profit at cost price, the ratio of water to milk must be 25:100 or 1:4. In a total mixture of 5 parts (1 water + 4 milk), water constitutes 1/5, which is 20%.

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