In a two-digit positive number, the unit digit is equal to the square of ten's digit. The difference between the original number and the number formed by interchanging the digits is 54. What is 40% of the original number?
 A) 15.6 B) 73 C) 84 D) None of the above

 A) 15.6

Let ten's digit be x and unit's digit be x2.

Original number = $$\Large 10x + x^{2}$$

New number = $$\Large 10x^{2} + x$$

According to the question,

=$$\Large 10x^{2} + x - 10x - x^{2} = 54$$

= $$\Large 9x^{2} - 9x = 54$$

= $$\Large 9 \left(x^{2} - x\right) = 54$$

= $$\Large x^{2} - x - 6 = 0$$

= $$\Large x^{2} - 3x + 2x - 6 = 0$$

= $$\Large x \left(x - 3\right) + 2 \left(x - 3\right) = 0$$

= $$\Large \left(x - 3\right) \left(x + 2\right) = 0$$

Therefore, x = 3, -2

Therefore, Ten's digit = x = 3

Unit's digit = $$\Large x^{2} = 3^{2} = 9$$

Original number = 39

Required number = $$\Large 39 \times \frac{40}{100} = 15.6$$

Similar Questions
1). In a three-digit number, the digit in the unit's place is four times the digit in the hundred's place. If the digit in the unit's place and the ten's place are interchanged, the new number so formed is 18 more than the original number. If the digit in the hundreds place is one-third of the digit in the ten's place, then what is 25% of the original number?
 A). 67 B). 84 C). 137 D). Couldn't be determined
2). The sum of the squares of two numbers is 97 and the squares of their difference is 25. The product of the two numbers is
 A). 45 B). 36 C). 54 D). 63
3). Consider the following statement: Inflation is an increase in the average level of prices. This implies that
1. The price of essential commodities outstrips income
2. Money supply grows at a higher rate than GDP in real terms
3. The exchange rate of a currency falls
4. Fiscal deficit exceeds balance of payment deficit.
Select the correct answer from the codes given below:
 A). 1, 2 and 4 only B). 2 only C). 1 and 4 only D). 1, 2,3 and 4
4). The existence of Black Money in the economy is recognized as a threat to the Indian economic system. Which of the following features is/are attributes of Black Money?
1. It refers to money generated through illegitimate means such as drug trade, crime, terrorism and corruption.
2. It includes counterfeit currency notes in circulation.
3. Wealth may have been generated through legitimate means but income thereon has not been declared nor the taxes due paid to the government.
4. None of the above.
Select the correct answer from the codes given below:
 A). 4 only B). 1, 2 and 3 only C). 3 only D). 1 and 3 only
5). Which of the following is not a reason for cost-push inflation?
 A). The payment of dearness allowance to employees B). The existence of a large parallel economy C). Fluctuations in agricultural and industrial output D). Excessive indirect taxation
6). Among the supply side measures to contain inflation is
 A). postponing public expenditure B). mopping up excess liquidity through taxation C). credit control measures of RBl D). maintaining price levels through an effective PDS
7). The purpose of central and state warehousing corporations is to
 A). distribute fertilizers and seeds B). to refinance farm credit C). provide storage facility D). process agricultural products
8). The rationale given in the first plan for state intervention in the industrial sector was that
 A). private sector was inefficient B). State alone can ensure decentralization of wealth C). Private sector was neither willing nor capable of investing in certain sectors D). The commanding heights of the economy should be in the public sector