Arithmetic

Ratio, Proportion & Variation

Medium

The sum of three numbers, namely, A, B and C is 156. The numbers A and B are in the ratio of 2:5, while B and C are in the ratio of 1:9. Find number B?

✅ Correct Option: 2

A and B are in the ratio 2:5.

$A = 2k$ and $B = 5k$ for some value $k$ .

B and C are in the ratio 1:9.

$B = m$ and $C = 9m$ for some value $m$ .

Since both expressions represent B:

$5k = m$

$C = 9m$

$C = 9(5k)$

$C = 45k$

All three numbers in terms of $k$ :

$A = 2k$

$B = 5k$

$C = 45k$

The sum equals 156:

$A + B + C = 156$

$2k + 5k + 45k = 156$

$52k = 156$

$k = 3$

$B = 5k$

$B = 5 \times 3$

$B = 15$

2026: 19 May Shift 2

IF A : B = $\frac{2}{9}$ : $\frac{1}{6}$ , B : C = $\frac{2}{7}$ : $\frac{5}{21}$ and D : C = $\frac{7}{10}$ : $\frac{3}{5}$ , D : E = $\frac{5}{7}$ : $\frac{3}{14}$

then

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	C : A	I.	32 : 7
B.	D : B	II.	24 : 7
C.	B : E	III.	35 : 36
D.	A : E	IV.	5 : 8

Choose the correct answer from the options given below:

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The sum of three numbers, namely, A, B and C is 156. The numbers A and B are in the ratio of 2:5, while B and C are in the ratio of 1:9. Find number B?

Solution

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