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A number when increased by 50 %', gives 2790. The number is:
5580
930
3720
1860
1860
Think of the number as 100%. Increasing it by 50% makes it 150%. 150% of x is 2790, so divide 2790 by 1.5 (or multiply by 2/3).
A number increased by 50% equals 2790. Let the original number be x.
x├Ч(1+10050тАЛ)=2790
Think of the number as 100%. Increasing it by 50% makes it 150%. 150% of x is 2790, so divide 2790 by 1.5 (or multiply by 2/3).
Students often calculate 50% of 2790 and subtract it (1395), failing to realize the increase was on the original number, not the final result.
Define the Equation
Let the original number be x. Increasing x by 50% means the new number is x+0.50x=1.5x. Given 1.5x=2790.
1.5x=2790
Solve for x
Isolate x by dividing 2790 by 1.5. To make it easier, multiply by 2/3: x=2790├Ч32тАЛ.
x=1.52790тАЛ=1860
Verification
Verify: 50% of 1860 is 930. Adding them: 1860+930=2790.
1860+930=2790
D is correct because 150% of 1860 is 2790.
This concept is identical to 'Profit %' calculations where (Cost Price + Profit = Selling Price). Mastering 1.5x, 1.25x, and 0.8x multipliers saves significant time in Profit/Loss and Discount chapters.
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