6. The monthly income of Santhosh and Vignesh together is Rs. 62500. The income of Santhosh and Vignesh is increased by 20% and 15% respectively. The new income of Vignesh is Rs. 1375 more than the new income of Santhosh. What is the new income of Vignesh?
A. Rs. 37375
B. Rs. 35625
C. Rs. 36500
D. Rs. 38250
Answer: Option A
Explanation:
Let the income of Santhosh and Vignesh be S and V,
The monthly income of Santhosh and Vignesh = 62500
S + V = 62500
Santhosh’s income = x; Vignesh’s income = 62500 – x
New income of V = New income of S + 1375
V’s new income = (62500 – x)*[latex]\frac{115}{100}[/latex]
S’s new income = x * [latex]\frac{120}{100}[/latex]
(62500 – x)* ([latex]\frac{115}{100}[/latex]) = x * ([latex]\frac{120}{100}[/latex]) + 1375
[latex]\frac{(7187500 – 115x)}{100}[/latex] = ([latex]\frac{120X}{1471x}[/latex]) + 1375
[latex]\frac{(7187500 – 115x)}{100}[/latex] = [latex]\frac{(120x + 137500)}{100}[/latex]
(7187500 – 115x) = (120x + 137500)
7187500 – 137500 = 115x + 120x
7050000 = 235x
Santhosh’s income X = [latex]\frac{7050000}{235}[/latex] = 30000
Vignesh’s income = 62500 – x = 32500
New Income of Vignesh = 32500*([latex]\frac{115}{100}[/latex]) = Rs. 37375
7. In a class 125 students, if the ratio of boys and girls in a class is 3: 2. If 24% of the boys and 20% of the girls are interested in dance, then find the % of students who are all not interested in dance?
A. 72.5 %
B. 75.8 %
C. 6 %
D. 65.6 %
Answer: Option C
Explanation:
Total no of students = 125
The ratio of boys and girls in a class = 3: 2 (3x, 2x)
Boys = 125*([latex]\frac{3}{5}[/latex]) = 75, Girls = 125*([latex]\frac{2}{5}[/latex]) = 50
24% of boys interested in dance = 75 * [latex]\frac{24}{100}[/latex] = 18
20% of girls interested in dance = 50 * [latex]\frac{20}{100}[/latex] = 10
Total number of students, who are all not interested in dance,
= > 125 – (18 + 10) = 125 – 28 = 97
Required % = ([latex]\frac{97}{125}[/latex]) * 100 = 77.6 %
8. The cost of a camera is Rs. 3500 more than that of a phone. 3 phone and 3 camera cost is Rs. 70500. Find the cost of a camera?
A. Rs. 14000
B. Rs. 13500
C. Rs. 15500
D. Rs. 12500
Answer: Option B
Explanation:
Let the cost of a phone be Rs. x
The cost of a camera = x + 3500
3*(x + 3500) + 3x = 70500
3x + 10500 + 3x = 70500
6x + 10500 = 70500
6x = 70500 – 10500
X = [latex]\frac{60000}{6}[/latex]
X = 10000
The cost of a phone = Rs. 10000
The cost of a camera = Rs. (10000 + 3500) = Rs. 13500
9. 15 % of monthly salary of P is equal to 30% of monthly salary of Q and 20 % of monthly salary of Q is equal to 30 % of monthly salary of R. If R’s monthly income is Rs. 40000, then the total income of P, Q and R is?
A. Rs. 227500
B. Rs. 235800
C. Rs. 215000
D. Rs. 220000
Answer: Option D
Explanation:
[latex]\frac{15P}{100}[/latex] = [latex]\frac{30Q}{100}[/latex] –> 1
[latex]\frac{20Q}{100}[/latex] = [latex]\frac{30R}{100}[/latex] –> 2
From 1, P = 2Q
From 2, 2Q = 3R (Here, R = 40000)
Q = [latex]\frac{(3*40000)}{2}[/latex] = 60000
P = 2Q = 2*60000 = 120000
P + Q + R = 120000 + 60000 + 40000
= > 220000
10. In a cricket between 2 teams, Team ‘x’ gets 70% of the total score and defeated team ‘y’ by 72 runs. The no of runs scored by the winner?
A. 260 runs
B. 190 runs
C. 182 runs
D. 126 runs
Answer: Option D
Explanation:
Team x = 70 %
Team y = 30 %
According to the question,
(70 % – 30 %) of the total score = 72
40 % of the total score = 72
(40/100)*total score = 72
Total score = 72*([latex]\frac{100}{40}[/latex] ) = 180
Total score get by the winner = 180*([latex]\frac{70}{100}[/latex] ) = 126 runs