11
Raju's monthly salary is 20 percent more than Anju’s monthly salary. Ravi’s monthly salary $150 more than Anju's salary. The sum of Raju, Anuj & Ravi’s yearly salaries is $32520. What is Raju’s annual salary?
A.
B.
C.
D.
Answer & Solution
Let, Anju’s monthly salary = $x
Then Raju’s monthly salary = $x × 120% = $1.20x
& Ravi’ monthly salary = $(x +150)
\ $(x + 1.20x + x+150)
× 12 = $32520
Þ 3.20x + 150 = 2710
Þ 3.2x = 2560
Þ x = 800
Hence, Raju’s annual salary = $1.2x × 12 =
$960 × 12 = $11520.
12
A sum of $6,100 was divided among 8 men, 10 women and 12 children in such a way that man received 25% more than a woman and each woman received 25% more than a child. How much did each woman receive?
A.
B.
C.
D.
Answer & Solution
Let, the amount received by each child be x.
Then amount received by each woman = 125% of x
= 5x/4
Amount received by each man = 125% of 5x/4 =
25x/16
\ 8 × (25x/16) + 10 ×
(5x/4) + 12x = 6100
Þ (25x/2) + (25x/2) +
12x = 6100
Þ 74x = 6100 × 2
Þ x = (6100 × 2)/74
Hence, amount received by each woman
=
{5(6100 × 2)}/(74 × 4)
= 7625/37
=
206.08
13
In an examination in which full marks were 800, A gets 20% more than B. B gets 20% more than C. an C gets 15% less than D. If A got 576, what percentage of full marks did D get (approximately)?
A.
B.
C.
D.
Answer & Solution
Let, D gets = 100
Then C gets = 100 × 85% = 85
B gets = 85 × 120% = 102
A gets = 102 × 120% = 122.4
Now, marks obtained by D = (576/122.4) × 100 =
470
\ % of full marks D got
= (470/800) × 100 = 58.8%
14
A train starts from station A with some passengers. At station B 10% of the passengers get down and 100 passengers get in. At station C 50% get down and 25 get in. At station D 50% get down and 50 get in making the total number of passengers 200 The number of passengers who boarded the train at station A was
A.
B.
C.
D.
Answer & Solution
To solve the problem, we shall follow back
calculation method:
At station D, after get in total passengers =
200
Before get in, total passengers = {(200 – 50)/50}
= 300 which is equal to total passengers after leaving station C.
At station C before get in total passengers =
{(300 – 25)/50} × 100 = 550 which is equal to passengers after leaving station
B.
At station B before get in total passengers =
{(550 – 100)/90} × 100 = 500.
15
In an examination, the percentage of students qualified to the number of students appeared from school A is 70%. In school B, the number of students appeared is 20% more than the students appeared from school A and the number of students qualified from school B is 50% more than the students qualified from school A. What is the percentage of students qualified to the number of students appeared from school B?
A.
B.
C.
D.
Answer & Solution
Let, the number of students appeared from
school A =100
Then number of students qualified from school
A = 70
Number of students appeared from school B =
120
Number of students appeared from school B =
(150/100) × 70
\ Required percentage =
(105/120) × 100 = 87.5%
16
The charges for a five-day trip by a cruise ship for one full ticket and a half-ticket are $1440 inclusive of boarding charges which are same for a full ticket and a half-ticket. The charges for the same trip for 2 full tickets and one half-ticket inclusive of boarding of the full ticket. Find the fare and the boarding charges are $2220 The fare for a half-ticket is 75% charges separately for one full ticket.
A.
B.
C.
D.
Answer & Solution
Let, the fare for full ticket be $x and
boarding charges be $y per ticket.
Then fare for a half ticket = 75% of x
= 3x/4
\ (x + y) + (3x/4 + y)
= 1440
Or, 7x – 8y = 5760 --------------- (i)
& 2(x + y) + (3x/4 + y) = 2220
Or.11x/4 + 3y = 2220
Or, 11x + 12y = 8880 --------------- (ii)
Solving equation (i) and (ii) we get, x = $480
& y = $300.
17
Alen pays income tax at the rate of 10%. If his Income increased by 10% and his tax rate increases to 15%, his net income would increase by $350. What is Alen's income?
A.
B.
C.
D.
Answer & Solution
Let, Alen’s income be $x
Then net income = (100 – 10)% of x
= 90% of x
= 9x/10
Now, Net income = 85% of 110% of x
= 85/100 × 110/100
× x
= 187x/200
\ 187x/200 – 9x/10 =
350
Or, 7x/200 = 350
Or, x = (350 × 200)/7
Or, x = 10000
18
Mr. Aultman, a businessman had the income in the year 2023, such that he earned a profit of 20% on his investment in the business. In the year 2024, his investment was less by $5000 but still had the same income (Income = Investment + Profit) as that in 2023. Thus, the percent profit earned in 2024 increased by 6%. What was his investment in 2023?
A.
B.
C.
D.
Answer & Solution
Let, Aultman’s investment in 2023 be $x
Then income in 2023 = ${x + 20% of x} = $120x/100=$1.2x
Income in 2024 = ${126/100(x – 5000)} =
$1.26(x – 5000)
\ 1.2x = 1.26(x – 5000)
Or, 1.26x – 1.2x = 6300
Or, 0.06x = 6300
Or, x = 105000
19
In a factory, producing parts for an automobile, the parts manufactured on the shop floor are required to go through three quality checks, each conducted after a specific part of the processing on the raw material is completed. Only parts that are not rejected at one stage are put through the subsequent stages of production and testing. If average rejection rates at these testing machines during a month are 10%, 5% and 2% respectively, then what is the effective rejection rate for the whole plant?
A.
B.
C.
D.
Answer & Solution
Let, the number of parts before the quality
checks be 100
Then number of parts passed after quality
checks
= (100 – 2)% of (100 – 5)% of
(100 – 10)% of 100
= 98% of 95% of 90% of 100
= 83.79%
\ Effective rejection
rate = (100 – 83.79) = 16.21%
20
Peter could save 10% of his income. But two years later when his income is increased by 20%, he could save the same amount only as before. By how much percent has his expenditure increased?
A.
B.
C.
D.
Answer & Solution
Let, original income = $100
Then, saving = $10 & expenditure = $90
New income = $120 & new savings = $10
So, new expenditure = $(120 – 10) = $110
Increase in expenditure = $(110- 90) = $20
\ Increase = (20/90 ×
100) = 22 2/9%
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