Categories

# [Smart Math] Ratio Proportion Problem 37

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

### Problem

What sum of money is divided between A, B and C; if B and C together get \$100 and C and A together get \$150 and A gets twice as much as B.

1. \$200
2. \$250
3. \$300
4. \$350
5. \$400

### The Usual Method

[contentblock id=google-adsense-post]

Let A, B and C individually get \$’1’, \$’2’ and \$’3’.

Hence,

$b+c=100$                                …… Eq. 1

$c+a=150$ and             …… Eq. 2

$a=2b$                                      …… Eq. 3

$\therefore a+b+2c=250$

$\therefore 2b+b+2c=250$

$\therefore 3b+2c=250$

$=b+(2b+2c)=250$

$2b+2c=200$                            ……From Eq. 1

$\therefore b+200=250$

from Eq. 1,

$\therefore a+b+c=100+50+50=200$ ……From Eq. 2

Hence total sum = \$200

(Ans: 1)

Estimated Time to arrive at the answer = 75 seconds.

### Using Technique

[contentblock id=google-adsense-post]

Simply by adding b + c = 100 and a + c = 150, we know that a + b+ 2c = 250. This means that a + b + c has to be less than a + b + 2c (i.e \$250). This eliminates all options except ‘1’.

(Ans: 1)

Estimated Time to arrive at the answer = 5 seconds.
[starrater tpl=10]

[contentblock id=smartmath-blockquote]