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# [Smart Math] Ratio Proportion Problem 34

Here’s and example of a SMART MATH problem for RATIO PROPORTION.

### Problem

\$ 190 is divided between A, B and C, so that A’s share is $1\frac{1}{2}$ times B’s and B’s is $1\frac{1}{2}$ times that of C’s. What is C’s share?

1. 90
2. 60
3. 40
4. 30
5. 20

### The Usual Method

A’s share = 1.5 times B’s

$\therefore$ A : B = 1.5 : 1

Also B’s share = 1.5 times C’s

$\therefore$ B: C = 1.5 : 1

$\therefore$A : B : C   =          1.5       :           1

aaaaaaaaaaaaaaaaaaaaaaaaaa 1.5       :           1

=          2.25     :           1.5       :           1

Hence C’s share = $190\times \frac{1}{1+1.5+2.25}$

$=190\times \frac{1}{4.75}=40$

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Partially ignoring the relationship between A, B and C, we can assume that A and B are both 1.5 times C. Hence, total proportion = 1.5 + 1.5 + 1 = 4

$\frac{190}{4}\approx 45$

But in reality, A is 1.5 times B. Hence the value of C has to be little less than 45. From amongst the options 40 is the only value that satisfies the condition.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.

Note: In the event of the options being close to 45 and less than that, just substitute the values as follows:

40 x 1 = 40

40 x 1.5 = 60

60 x 1.5 = 90

Sum: 40 + 60 + 90 = 190, which satisfies the conditions, so option ‘3’ is the answer.
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