The sum of three numbers in G.P. is 70 . If the two extremes by multiplied each by 4 and the mean by 5 , the products are in AP. The numbers are

Option b: 10, 20, 40. Solution: Let the three numbers in G.P. be a, ar, ar2 . Their sum is 70 : a(1+r+r2) = 70 --- (1) Multiplying extremes by 4 and mean by 5 gives 4a, 5ar, 4ar2 in A.P.: 2(5ar) = 4a + 4ar2 10ar = 4a(1+r2) 5r = 2(1+r2) 2r2 - 5r + 2 = 0 (2r-1)(r-2) = 0 r = 2 or r = 1/2 If r=2 , from (1): 7a = 70 a = 10 . The numbers are 10, 20, 40 . Hence, Option B is the correct answer.

The sum of three numbers in G.P. is $70$. If the two extremes by multiplied each by $4$ and the mean by $5$, the products are in AP. The numbers are

The correct answer is Option b: $10, 20, 40$. Let the three numbers in G.P. be $a, ar, ar^2$. Their sum is $70$: $$a(1+r+r^2) = 70 \quad \text{--- (1)}$$ Multiplying extremes by $4$ and mean by $5$ gives $4a, 5ar, 4ar^2$ in A.P.: $$2(5ar) = 4a + 4ar^2$$ $$10ar = 4a(1+r^2)$$ $$5r = 2(1+r^2) \implies 2r^2 - 5r + 2 = 0$$ $$(2r-1)(r-2) = 0 \implies r = 2 \text{ or } r = \frac{1}{2}$$ If $r=2$, from (1): $7a = 70 \implies a = 10$. The numbers are $10, 20, 40$. Hence, **Option B** is the correct answer.

Sequence and SeriesMCQMTP May 20Question 1880 of 212

All Questions

The sum of three numbers in G.P. is $\displaystyle 70$ . If the two extremes by multiplied each by $\displaystyle 4$ and the mean by $\displaystyle 5$ , the products are in AP. The numbers are

Options

\displaystyle 12, 18, 40

\displaystyle 10, 20, 40

\displaystyle 40, 20, 15

DNone of these

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Correct Answer

✅ Option b — $\displaystyle 10, 20, 40$

All Options:

A $\displaystyle 12, 18, 40$
B $\displaystyle 10, 20, 40$
C $\displaystyle 40, 20, 15$
DNone of these

Detailed Solution & Explanation

Let the three numbers in G.P. be

\displaystyle a, ar, ar^2

.
Their sum is

\displaystyle 70

a(1+r+r^2) = 70 \quad \text{--- (1)}

Multiplying extremes by

\displaystyle 4

and mean by

\displaystyle 5

gives

\displaystyle 4a, 5ar, 4ar^2

in A.P.:

2(5ar) = 4a + 4ar^2

10ar = 4a(1+r^2)

5r = 2(1+r^2) \implies 2r^2 - 5r + 2 = 0

(2r-1)(r-2) = 0 \implies r = 2 \text{ or } r = \frac{1}{2}

\displaystyle r=2

, from (1):

\displaystyle 7a = 70 \implies a = 10

. The numbers are

\displaystyle 10, 20, 40

.
Hence, **Option B** is the correct answer.

About This Chapter: Sequence and Series

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Arithmetic & Geometric Progressions

This chapter covers Arithmetic Progressions (AP) and Geometric Progressions (GP). Students learn how to find the nth term, sum of n terms, arithmetic/geometric means, and sum to infinity of a GP.

View Official ICAI Syllabus

Exam Strategy Tip

For complex 'sum of series' questions, a great hack is to substitute n = 1 and n = 2 into the question and the options to see which one matches, completely bypassing the formula.

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The sum of three numbers in G.P. is 70\displaystyle 7070. If the two extremes by multiplied each by 4\displaystyle 44 and the mean by 5\displaystyle 55, the products are in AP. The numbers are