**Problem 1 :**

A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation ?

**Solution :**

In the given two fractions, the denominators are 5 and 3.

Let assume a number which is divisible by both 5 and 3.

Least common multiple of (5, 3) = 15.

So, let the number be 15.

15 ⋅ 3/5 = 9 ----- (1) -----> incorrect

15 ⋅ 5/3 = 25 -----(2) -----> correct

Difference between (1) and (2) is 16

Percentage error is

= (Actual error / Correct answer) ⋅ 100 %

= (16 / 25) ⋅ 100 %

= 64 %

Hence, the percentage error in the calculation is 64 %.

**Problem 2 :**

There are 15 boys and 12 girls in a section A of class 7. If 3 boys are transferred to section B of class 7,then find the percentage of boys in section A.

**Solution :**

**Before transfer :**

No. of boys in section A = 15

No. of boys in section B = 12

Given : 3 boys are transferred from section A to B

**After transfer :**

No. of boys in section A = 12

No. of boys in section B = 12

Hence, percentage of boys in section A is 50%

**Problem 3 :**

If there are 3 boys and 7 girls in a class then, what percent of the class is made up of boys ?

**Solution :**

Total number of students in the class = 3 + 7 = 10

Percentage of boys is

= (No. of boys / Total no. of students) ⋅ 100 %

= (3/10) ⋅ 100 %

= 30 %

Hence, 30 % of the class is made up of boys.

**Problem 4 :**

Two numbers are respectively 20% and 50% are more than a third number, Find the the ratio of the two numbers.

**Solution :**

Let x be the third number.

Then,

the first number = (100+20)% of x = 120% of x = 1.2x

the first number = (100+50)% of x = 150% of x = 1.5x

First no. : Second no. = 1.2x : 1.5x

Multiply both the terms of the ratio by 10.

First no. : Second no. = 12x : 15x

Divide both the terms of the ratio by 3x.

First no. : Second no. = 4 : 5

Hence, the ratio of the two number is 4 : 5.

**Problem 5 :**

In a triangle, the first angle is 20% more than the third angle. Second angle is 20% less than the third angle. Then find the three angles of the triangle.

**Solution :**

Let x be the third angle.

Then,

first angle = 120% of x = 1.2x

second angle = 80% of x = 0.8x

Sum of the three angles in any triangle = 180°

Then, we have

x + 1.2x + 0.8x = 180°

3x = 180°

x = 60°

Then,

first angle = 1.2(60°) = 72°

second angle = 0.8(60°) = 48°

Hence, the three angles of the triangle are 72°, 60° and 48°.

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