# Number Theory

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**Q6.**If (5x - 3)3+ (3x - 5)3+ (3x - 1)3= 45 (x -(frac 3 5)) (3x - 5) (x - (frac 1 3)), then what will be the value of ((frac 11 9)x + 5)3?

**Q8.**The sum of two numbers is 22 & the sum of their squares is 404, then the sản phẩm of those numbers is :

**Q2.**The denominator of a fraction is 4 more than twice the numerator. When both the numerator & denominator are decreased by 6, then the denominator becomes 12 times the numerator. Determine the fraction.

**Q4.**A woman had only 50 paisa và 1 rupee coins in her purse. The total number of coins were 120 & the total amount was Rs.100. So the number of 1 rupee coins are_______.

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**Q6.**Find the units digit in 676 × 376 × 437 × 913 × 423 × 337 × 421.

**Q7.**You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.Question: What is the value of 'Y'?Statements:(1) 29X +12Y = 528(2) 145X + 60Y = 2640

**Q1.**In 1 kg. Mixture of sand và iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10% ?

**Q2.**In an exam, a student gets 20% marks và fails by 30 marks. A second student scores 32% marks but gets 42 marks more than the minimum passing marks. Find the passing percentage?

**Q5.**A train 100 metres long, moving at a tốc độ of 50 km per hour, crosses another train 120 metres long coming from the opposite direction in 6 seconds. What is the speed of the second train?

**Q6.**A train leaves Meerutat 5 a.m. And reaches Delhi at 9 a.m. Another train leaves Delhi at 7 a.m. & reaches Meerutat 10:30 a.m. At what time vị the two trains cross each other?

**Q7.**The simple interest on a certain sum of money at the rate of 5 p.a. For 8 years is Rs. 840. The rate of interest for which the same amount of interest can be received on the same sum after 5 years is

**Q8.**The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre.

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**Q9.**94 is divided into two parts in such a way that the fifth part of the first & the eighth part of the second are in the ratio 3 : 4 The first part is:

**Q10.**The denominator of a fraction is 4 more than twice the numerator. When both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. Determine the fraction.