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Parin Sir > Quantitative Aptitude (Maths) > Ratio Proportion & Variation > Examples 1 to 5 > Examples 1 to 5

Examples 1 to 5

June 16, 2020
Category: Examples 1 to 5

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(1) If a : b = 3 : 10 and b : c = 15 : 7, find a : c & a : b : c.

Soln. a : b = 3 : 10 & b : c = 15 : 7

a : b = 3 : 10

= 9 : 30

b : c = 15 : 7

= 30 : 14

a : b : c = 9 : 30 : 14 $\large \Rightarrow$ a : c = 9 : 14

a : c = $\frac{a}{c}$ = $\frac{a}{b}\times \frac{b}{c}$ = $\frac{3}{10}\times \frac{15}{7}$ = $\frac{9}{14}$ = 9 : 14

(2) Divide Rs. 2010 between A, B and C, so that for every Rs. 5 A receives, B receives Rs. 3 and for every Rs. 4 A receives, C receives Rs. 7.

Soln. A : B = 5 : 3 & A : C = 4 : 7

$\therefore$ A : B = 5 : 3

= 20 : 12 A : C = 4 : 7

= 20 : 35

A : B : C = 20 : 12 : 35

A’s share = $\frac{20}{67}\times$ 2010 = Rs. 600

B’s share = $\frac{12}{67}\times$ 2010 = Rs. 360

C’s share = $\frac{35}{67}\times$ 2010 = Rs. 1050

(3) The number 300 is divided so that $\frac{1}{4}$ times the first part and $\frac{1}{7}$ times the second part is in the ratio 3 : 4. What is the first part ?

Soln. Let X be the first part and Y be the second part.

$\therefore$ Here, $\frac{\frac{1}{4}x}{\frac{1}{7}y}=\frac{3}{4}$

$\therefore$ $\frac{x}{y}$ = $\frac{3}{4}\times \frac{4}{1} \times \frac{1}{7}$ = $\frac{3}{7}$

$\therefore$ 1^st part = X = $\frac{3}{10}\times$ 300 = 90.

(4) If a : b = 3 : 7, find ( 3a + 5b ) : ( 7a – 2b ).

Soln. Here, a : b = 3 : 7 a = 3k and b = 7k.

Now, $\frac{3a+5b}{7a-2b}$ = $\frac{3\left (3k \right )+5\left (7k \right )}{7\left (3k \right )-2\left (7k \right )}$

= $\frac{44k}{7k}$ = $\frac{44}{7}$ .

Hence, ( 3a + 5b ) : ( 7a – 2b ) = 44 : 7

(5) Divide 500 among A, B, C so that 10A = 15B = 6C.

Soln. Here, 10A = 15B = 6C $\large \Rightarrow$ $\frac{10A}{30}$ = $\frac{15B}{30}$ = $\frac{6C}{30}$ $\large \Rightarrow$ $\frac{A}{3}$ = $\frac{B}{2}$ = $\frac{C}{5}$