Question

a man got a 10% increase in his salary.if has new salary is 154000 find its original salary (maths)



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Answer 1

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Step-by-step explanation:

Hint:

To solve this question, we have to assume his original salary as x. It is given that he has got a 10% increase in his salary. If a number ‘y’ is increased by k%, it means that ‘y’ is increased by k% of ‘y’. Numerically, ‘y’ is increased by k% of ‘y’ can be written as y+(k100×y). Using this relation, by substituting y = x and k = 10 and equating the increased value to Rs.154000, we get the value of the x that is his original salary.

Complete step-by-step answer:

Let the salary of the man is Rs. x. In the question, it is given that he has got an increment of 10% in his salary and the final salary is Rs.154000.

If a number ‘y’ is increased by k%, it means that ‘y’ is increased by k% of ‘y’. Numerically, ‘y’ is increased by k% of ‘y’ can be written as y+(k100×y).

By substituting y = x and k = 10 and equating it to 154000, we get

Incremented value = 154000=x+(10100×x)=x+0.1x=1.1x

Dividing by 1.1, we get

x=1540001.1=154000×1011=154000011=11×1400001

1=140000

∴ The original salary of the person is Rs. 140000.

Note:

Students can make a mistake by thinking that subtracting 10% from the final salary gives the initial salary. In other words, they think that Rs. 154000 – 10% of 154000 gives the value of original salary. This thinking leads to an answer of 154000−10100×154000=154000−15400=138500. This is wrong because the 10% of original salary is not equal to 10% of the final salary and the increase of 10% in original salary is not equal to decrease of 10% in final salary

Answer 2

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Let, the salary before the increment be Rs.100. Then,

Increase in salary =Rs.10

∴ Increased salary =Rs.(100+10) = Rs.110

If increased salary is Rs. 110, original salary =Rs.100

If increased salary is Rs. 154000, original salary =Rs$\rm{( \frac{100}{110} \times 154000) }=Rs140000$

Hence, the salary of the man before increment was Rs.140000.