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Ratio and Proportion
1.If a:b:c = 3:4:7, then the ratio (a+b+c):c is equal to

Explanation:

Solution:
(a+b+c) = 3+4+7 = 14 and
c = 7 Then, (a+b+c):c = 2:1.

2.The number of students in 3 classes is in the ratio 2:3:4. If 12 students are increased in each class this ratio changes to 8:11:14. The total number of students in the three classes in the beginning was

Explanation:

Solution:
Let the number of students in the classes be 2x, 3x and 4x respectively;
Total students = 2x+3x+4x = 9x.
$\begin{array}{rl}& \text{According}\phantom{\rule{thinmathspace}{0ex}}\text{to}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{question},\\ & \frac{\left(2x+12\right)}{\left(3x+12\right)}=\frac{8}{11}\\ & 24x+96=22x+132\\ & Or,\phantom{\rule{thinmathspace}{0ex}}2x=132-96\\ & Or,\phantom{\rule{thinmathspace}{0ex}}x=\frac{36}{2}=18\\ & \text{Nence,}\\ & \text{Original}\phantom{\rule{thinmathspace}{0ex}}\text{number}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}\text{students},\\ & 9x=9×18\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=162\end{array}$

3.A box has 210 coins of denominations one-rupee and fifty paise only. The ratio of their respective values is 13:11. The number of one-rupee coin is

Explanation:

Solution:
Respective ratio of the number of coins;
= 13:11*2 = 13:22
Hence, Number of 1 rupee coins;
= 13*210/(13+22) = 78.

4.If A and B are in the ratio 3:4, and B and C in the ratio 12:13, then A and C will be in the ratio

Explanation:

Solution:
$\begin{array}{rl}& \left(\frac{A}{B}\right)×\left(\frac{B}{C}\right)=\left(\frac{3}{4}\right)×\left(\frac{12}{13}\right)\\ & Or,\phantom{\rule{thinmathspace}{0ex}}\frac{A}{C}=\frac{36}{52}=9:13\end{array}$

5.The salaries of A, B and C are in the ratio 1:3:4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio

Explanation:

Solution:
Let A's Salary = Rs. 100
Then, B's Salary = Rs. 300
And, C's Salary = Rs 400
Salary has given in 1:3:4 ratio.
Now,
5% increase in A's Salary,
A's new Salary = (100 + 5% of 100) = Rs. 105.
B's Salary increases by 10%, Then,
B's new Salary = (300 + 10% of 200) = Rs. 330.
C's Salary increases by 15%,
C's new Salary = (400 + 15% of 400) = Rs. 460.
Then, ratio of increased Salary,
A:B:C = 105:330:460 = 21:66:92.

Alternative
100(A's salary)===5%↑===> 105(A's increased salary);
300 (B's salary)===10%↑===>330 (B's increased salary);
400 (C's salary)===15%↑===> 460 (C's increased salary).
Ratio of their increased salary = 105:330:480 = 21:66:92

6.If A:B = 2:3 and B:C = 4:5 then A:B:C is

Explanation:

Solution:

A/B = 2/3;
B/C = 4/5;
A:B:C = 2*4:3*4:3*5 = 8:12:15.

7.If two times A is equal to three times of B and also equal to four times of C, then A:B:C is

Explanation:

Solution:
$\begin{array}{rl}& 2A=3B\\ & Or,\phantom{\rule{thinmathspace}{0ex}}B=\left(\frac{2}{3}\right)A;\phantom{\rule{thinmathspace}{0ex}}\text{and}\\ & 2A=4C\\ & Or,\phantom{\rule{thinmathspace}{0ex}}C=\left(\frac{1}{2}\right)A;\\ & \text{Hence},\\ & A:B:C=A:\frac{2A}{3}:\frac{A}{2}\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=1:\frac{2}{2}:\frac{1}{2}\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=6:4:3\end{array}$

8.Two numbers are in ratio 4:5 and their LCM is 180. The smaller number is

Explanation:

Solution:
Let two numbers be 4x and 5x;
their LCM = 180 and HCF = x; Now,
1st number * 2nd number = LCM*HCF
Or, 4x*5x = 180*x;
Or, 20x = 180;
Or, x = 9;
then, the smaller number = 4*9 = 36.

9.If A:B = 2:3, B:C = 4:5 and C:D = 5:9 then A:D is equal to:

Explanation:

Solution:
$\begin{array}{rl}& \frac{A}{D}=\left(\frac{A}{B}\right)×\left(B×C\right)×\left(\frac{C}{D}\right)\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=\left(\frac{2}{3}\right)×\left(\frac{4}{5}\right)×\left(\frac{5}{9}\right)\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=\frac{\left(2×4×5\right)}{\left(3×5×9\right)}\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=\frac{8}{27}\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=8:27\end{array}$

10.In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is