61. In an Entrance Examination Ritu scored 56 percent marks, Smita scored 92 percent marks and Rina scored 634 marks. The maximum marks of the examination are 875. What are the average marks scored by all the three girls together?
(a) 1929
(b) 815
(c) 690
(d) 643
(e) None of these.
Solution: (d)
Marks scored by Ritu = \(\displaystyle 875\times \frac{{56}}{{100}}=490\)
Marks scored by Smita = \(\displaystyle 875\times \frac{{92}}{{100}}=805\)
Therefore, Average marks scored by all the three together =\(\displaystyle \frac{{490+805+634}}{3}=\frac{{1929}}{3}=643\)
62. The sum of 55% of a number and 40% of the same number is 180.5. What is 80% of that number?
(a) 134
(b) 152
(c) 148
(d) 166
(e) None of these
Solution: (b)
Let the number be x.
Now (55 + 40)% of x = 180.5
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{x\times 95}}{{100}}=180.5\)
x= \(\displaystyle \frac{{180.5\times 100}}{{95}}=190\)
Now 80% of 190 = \(\displaystyle \frac{{190\times 80}}{{100}}=152\)
63. In an examination it is required to get 65% of the aggregate marks to pass, A student gets 847 marks and is declared failed by 10% marks. What are the maximumaggregate marks a student can get?
(a) 1450
(b) 1640
(c) 1500
(d) Cannot be determined
(e) None of these
Solution: (e)
Let maximum marks = x
Student got 55% x = 847
Therefore, x = \(\displaystyle x=\frac{{847\times 100}}{{55}}=1540\)
64. Last year there were 610 boys in a school. The number decreased by 20 percent this year. How many girls are there in the school if the number of girls is 175 percent of the total number of boys in the school this year?
(a) 854
(b) 848
(c) 798
(d) 782
(e) None of these
Solution: (a)
No. of boys, last year = 610
20% of 610 = 122 No. of boys, current year = 610 – 122 = 488
No. of girls = 175% of 488
= \(\displaystyle \frac{{175\times 488}}{{100}}=854girls\)
65. 855 candidates applied for a job, out of which 80% of the candidates were rejected. How many candidates were selected for the job?
(a) 684
(b) 151
(c) 676
(d) 179
(e) None of these
Solution: (e)
No. of candidates selected for job = 20% of 855
\(\displaystyle \frac{{20\times 855}}{{100}}=171\)
65. What should come in place of the question mark so that it satisfies equality of the equation — 32% of 750 < ?
(a) 23% of 600
(b) 46% of 207
(c) 98% of 250
(d) 75% of 320
(e) None of these
Solution: (c)
32% of 750=\(\displaystyle \frac{{32\times 750}}{{100}}=240\)
23% of 600 =\(\displaystyle \frac{{23\times 600}}{{100}}=138\)
46% of 207 =\(\displaystyle \frac{{46\times 207}}{{100}}=95.22\)
98% of 250 =\(\displaystyle \frac{{98\times 250}}{{100}}=245\)
66. Sum of three consecutive numbers is 2262. What is 41 % of the highest number?
(a) 301.51
(b) 303.14
(c) 308.73
(d) 306.35
(e) 309.55
Solution: (e)
Let the numbers are x, x + 1, x + 2
Sum of three consecutive numbers = 2262
x + x + 1 + x + 2 = 2262
3x + 3 = 2262
3x = 2259
x = 753
Number are 753, 754, 755
Therefore, 41% of 755 = 309.55
67. In an examination, Raman scored 25 marks less than Rohit. Rohit scored 45 more marks than Sonia. Rohan scored 75 marks which is 10 more than Sonia. Ravi’s score is 50 less than, maximum marks of the test. What approximate percentage of marks did Ravi score in the examination, if he gets 34 marks more than Raman?
(a) 90
(b) 70
(c) 80
(d) 60
(e) 85
Solution: (b)
Rohan’s marks = 75
Sonia’s marks = 65
Rohit’s marks = 65 + 45 = 110
Raman’s marks = 110 – 25 = 85
Ravi got marks = 85 + 34 = 119
Total maximum marks = 119 + 50 + 169
Percentage of Ravi’s marks= \(\displaystyle \frac{{119}}{{169}}\times 100\%=70.4\%=70\%\)
68. 10% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.
(a) 5000
(b) 6000
(c) 7000
(d) 8000
(e) None of these
Solution: (b)
Let the total number of original inhabitants be x. Then,
(100 – 25)% of (100 –10)% of x = 4050
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{75}}{{100}}\times \frac{{90}}{{100}}\times x=4050\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{27}}{{40}}x=4050\)
\(\displaystyle \Rightarrow \)\(\displaystyle x=\frac{{4050\times 40}}{{27}}=6000\)
Number of original inhabitants = 6000.
69. ‘A’ sells a good to ‘B’ at a profit of 20 % and ‘B’ sells it to C at profit of 25 %. If ‘C’ pays ₹ 225 for it, what was cost price for ‘A’ ?
(a) 150
(b) 120
(c) 200
(d) 110
(e) None of these
Solution: (a)
During both the transaction there are profits. So our calculating figures would be 120, 125 and 100. A’s cost is certainly less than C’s selling price
Therefore, Required price = \(\displaystyle 225\times \frac{{100}}{{120}}\times \frac{{100}}{{125}}=150\)
70. Naresh’s monthly income is 30% more than that of Raghu. Raghu’s monthly income is 20% less than that of Vishal. If the difference between the monthly incomes of Naresh and Vishal is ₹ 800, what is the monthly income of Raghu?
(a) ₹ 16,000
(b) ₹ 20,000
(c) ₹ 12,000
(d) Data inadequate
(e) None of these
Solution: (a)
N = R + 30% of R = 1.3 R
R = V – 20% of V = 80% of V = 0.8 V
Therefore, N = 1.3 × 0.8V = 1.04 V
Now, N – V = 1.04 V – V = 0.04 V = ₹800 (given)
Therefore, V = ₹ 20000
Hence, R = 0.8 × 20000 = ₹16000
