Question

The sum of three numbers is 174. The ratio of 2nd and 3rd number is 9:16 and the ratio of 1st and 3rd number is 1 : 4 The 2nd number is :-
(1)24
(2)20
(3) 54
(4)30​

Answer 1

Answer

54, option (3)

$\rule{50}2$

Explanation

Beauty of maths is unknown, so let the three numbers be x, y and z.

Now, given that the ratio of 2nd and 3rd number is 9:16

→ $\sf\frac{y}{z} = \frac{9}{16}$

→ $\sf y = \frac{9z}{16}$ ....(1)

And, the ratio of the 1st and 3rd number is 1:4

→$\sf\frac{x}{z} = \frac{1}{4}$

→$\sf z = 4x$ ......(2)

Put value of z as 4x in (1)

→ $\sf y = \frac{9\times 4x}{16}$

→ $\sf y = \frac{9x}{4}$

Now, we get that y = 9x/4 and z = 4x. We know that

x + y + z = 174 (given)

So, put the values of y and z in term of x

→ $\sf x + \frac{9x}{4} + 4x = 174$

→ $\sf \frac{4x + 16x + 9x}{4} = 174$

By cross multiplying,

4x + 16x + 9x = 174 × 4

→ 29x = 696

→ x = 696/29

→ x = 24

Now, since y = 9x/4, we get

y = 9/4 × 24

→ y = 9 × 6

→ y = 54.

Hence, the second number (y) is 54.

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore 2nd\:number=54}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about the sum of three numbers is 174. The ratio of 2nd and 3rd number is 9:16 and the ratio of 1st and 3rd number is 1 : 4.

• We have to find the 2nd number.

$\underline \bold{Given : } \\ \implies a + b + c = 174 \\ \\ \implies b : c = 9 : 16 \\ \\ \implies a : c = 1 : 4 \\ \\ \underline \bold{To \: Find : } \\ \implies b = ?$

• According to given question :

$\bold{For \: ratio \: of \: 2nd \: and \: 3rd \: no.} \\ \implies \frac{b}{c} = \frac{9}{16} \\ \\ \implies 9c = 16b \\ \\ \implies c = \frac{16b}{9} - - - - - (1) \\ \\ \bold{For \: ratio \: of \: 1st \: and \: 3rd \: no.} \\ \implies \frac{a}{c} = \frac{1}{4} \\ \\ \implies c = 4a - - - - - (2) \\ \\ \bold{Equating \: both \: the \: equation :} \\ \implies \frac{16b}{9} = 4a \\ \\ \implies \frac{a}{b} = \frac{4}{9} \\ \\ \implies b = \frac{9a}{4} - - - - - (3) \\ \\ \implies a + b + c = 174 \\ \\ \implies a + \frac{9a}{4} + 4a = 174 \\ \\ \implies \frac{4a + 9a + 16a}{4} = 174 \\ \\ \implies 29a = 174 \times 4 \\ \\ \implies a = \frac{174 \times 4}{29} \\ \\ \bold{\implies a = 24} \\ \\ \bold{Putting \: value \: of \: a \: in \: (3) \:we \: get } \\ \implies b = \frac{9a}{4} \\ \\ \implies b = \frac{9 \times \cancel{24}}{ \cancel4} \\ \\ \bold{\implies b = 54}$