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# [Smart Math] Ratio Proportion Problem 14

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

### Problem

The ratio of the number of boys and girls in a school 432 students is 5 : 4. How many new girls should join the school so that the ratio becomes 1 : 1?

1. 16
2. 48
3. 62
4. 244
5. 320

### The Usual Method

The number of boys in the school = $\frac{5}{5+4}\times 432=240$

The number of girls in the school = $\frac{4}{5+4}\times 432=192$

For the ratio of boys and girls to become 1 : 1, the number of new girls that join the school should be = 240 – 192 = 48

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

To have equal number of boys and girls, the ratio of boys to girls should change from 5 : 4 to 1 : 1. Also, 1 : 1 is equivalent to 5 : 5. The number of boys = 5x and the number of girls = 5x. Hence total number of students = 10x.

This means that the total number of students after new girls join is a multiple of 10 and hence the last digit of the sum should be = 0.

The existing total number of students = 432 with last digit = 2. Hence, the last digit of the number of girls who join should have last digit = 8, to get the last digit of the final sum = 0. The only option satisfying this condition is option ‘2’.

(Ans: 2)

Estimated Time to arrive at the answer = 10 seconds.
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